measurement and modelling of water use of citrus …

MEASUREMENT AND MODELLING OF WATER USE OF CITRUS ORCHARDS

By

WALTER MAHOHOMA

A thesis submitted in fulfilment of the requirements for the degree of PhD in

Agronomy

In the Faculty of Natural and Agricultural Sciences

University of Pretoria

Supervisor: Dr NJ Taylor

Co-Supervisor: Prof. JG Annandale

April 2016

© University of Pretoria

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Acknowledgements

My sincere gratitude goes to my supervisors Dr NJ Taylor and Professor JG

Annandale for the guidance throughout the course of my study. The CSIR staff who

worked on the “Water use of fruit trees” project who are Dr MB Gush, Dr AD Clulow,

Mr V Naiken and Dr MG Mengistu for all the assistance. I am also thankful to my

colleagues in the water group in the department for all the assistance. I am also

grateful to Dr S Dzikiti for his advice throughout the writing of this thesis.

The project would not be possible without the understanding of Moosrivier Farm

(Schoeman Boerdery Group) staff who provided the facilities for carrying out this

project especially Messrs J Burger, H Schoeman and B du Toit we worked with.

My sincere gratitude also goes to all the staff at the University of Pretoria Farm for

the support especially Mr L Nonyane and Mr L van Merwe. Sencere gratitude to my

colleagues Nadia Ibramo, Solomon Ghezehei, Melake Fessehazion and Godwill

Madamombe for the support. I also would like to thank members of the Agronomy

Department at Midlands State University for the support.

I gratefully acknowledge the Water Research Commission (WRC) and South African

Department of Agriculture for providing all the financial support throughout the

course of my study.

Last but not least much love goes to my wife (Tsungai), two brothers (Webster and

Wellington), and two sisters (Sekai and Longina (RIP)), together with their families

for their unwavering support.


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Declaration

I, Walter Mahohoma, declare that the dissertation, which I hereby submit for the

degree PhD Agronomy at the University of Pretoria, is my own work and has not

previously been submitted by me for a degree at another university. Where

secondary material is used, this has been carefully acknowledged and referenced in

accordance with university requirements. I am aware of university policy and

implications regarding plagiarism.

Walter Mahohoma

Date: 15 September 2016


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Abstract

MEASUREMENT AND MODELLING OF WATER USE OF CITRUS ORCHARDS

By

Walter Mahohoma

Supervisor: Doctor NJ Taylor

Co-supervisor: Professor JG Annandale

Degree: PhD Agronomy

Water requirements of evergreen citrus orchards in semi-arid regions of the world

are mostly met through irrigation. Definitive knowledge of crop water use is the

fundamental basis for sound water management under these production systems.

The objectives of this study were two-fold: i) to measure long-term transpiration of

well managed micro-irrigated citrus orchards and; ii) to test physically–based models

that can be used to predict transpiration across different citrus growing regions.

Whole tree transpiration measurements were conducted using the heat ratio method

(HRM) sap flow technique in two well-irrigated citrus orchards [Citrus sinensis (L.)

Osbeck] in the summer rainfall area of South Africa. The two orchards planted with

‘Delta’ Valencia and ‘Bahianinha’ Navel orange trees were located at Moosrivier

Farm in Groblersdal. A data set from an orchard planted with ‘Rustenburg’ Navel

orange trees that was located in the winter rainfall area was sourced for model

validation. The orchard was located at Patrysberg Farm in the winter rainfall area. All

the orchards were drip irrigated and managed according to the industry standards.

Weather parameters were monitored using automatic weather stations that were

situated close to the fields, for modelling purposes.

The HRM was initially calibrated against eddy covariance measurements in winter

(31July to 3 August 2008) and autumn (21 to 25 May 2009) in the ‘Delta’ Valencia

orchard, when soil evaporation was considered negligible. Calibration was done by

adjusting the wounding width to ensure that average transpiration of sample trees

matched crop evapotranspiration (ETc) measured above the orchard using the eddy

covariance method. The wounding width, termed the ‘virtual wound width’, was

obtained by inputting ETc into regression equations of daily transpiration against


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wound width. Xylem anatomical assessments were conducted on excised stem

samples prior to probe insertion and at the conclusion of sap flow measurements in

in order to ascertain and explain the virtual wound width determined through

calibration. The average virtual wound width that matched average transpiration of

sample trees to ETc in both winter and autumn was 3.2 mm. The similarity of the

virtual wound width obtained during winter and autumn suggests that wounding did

not increase with time and a single field calibration of the HRM using eddy

covariance measurements is sufficient for measuring long term transpiration in citrus

orchards.

The HRM was used to measure transpiration for periods of 364 days in the ‘Delta’

Valencia orchard, 301 days in the ‘Bahianinha’ Navel orchard and 365 days in the

‘Rustenburg’ Navel orchard. Average transpiration in the ‘Delta’ Valencia orchard

was 1.15 mm day-1 and 2.17 mm day-1 in winter and summer, respectively. On

average, ‘Bahianinha’ Navel orange trees transpired 0.77 mm day-1 and 1.69 mm

day-1 in winter and summer, respectively. In the ‘Rustenburg’ Navel orchard average

transpiration was 2.26 mm day-1 for summer and 2.08 mm day-1 for winter. Total

transpiration measured in the ‘Delta’ Valencia, ‘Bahianinha’ and ‘Rustenburg’ Navel

orchards was 650, 433 and 682 mm, respectively. Transpiration coefficients (Kt)

determined in the three orchards ranged between 0.28 and 0.71. The Kt values were

almost constant throughout the seasons in the summer rainfall area and significantly

higher in the winter months than in the summer months in the winter rainfall area.

Derived monthly and seasonal Kt determined for the three orchards were much lower

than the standardised values published in the FAO56. Differences among the

transpiration coefficients determined in the orchards in this study means that they

are orchard specific and can therefore not be directly applied or transferred to

different growing regions of the world.

There is a need to develop an easy method for estimating site-specific crop

coefficients, in order to improve water management in citrus orchards. The

determination of basal crop coefficients based on physical characteristics of the

vegetation and an adjustment for relative crop stomatal control over transpiration

formulated by Allen and Pereira (2009) was tested. Use of the parameters for

generic citrus trees suggested by the authors did not provide good estimates of


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transpiration in the three study orchards. A good agreement between measured and

estimated Kt values was obtained by back-calculating leaf resistances using

measured transpiration values, as recommended by Allen and Pereira (2009). The

values of leaf resistances obtained through this procedure were higher than the

values suggested by Allen and Pereira (2009), but comparable to those reported in

literature and measured in the ‘Rustenburg’ navel orchard. A relationship between

mean monthly leaf resistance and ETo in the ‘Rustenburg’ Navel orchard provided a

means of estimating mean leaf resistance which estimated Kt values with a

reasonable degree of accuracy in the three orchards. However, this relationship only

provided good seasonal estimates of transpiration, which means that it can only be

useful for irrigation planning.

A more mechanistic model capable of capturing the dynamics of the canopy

conductance in citrus varieties is required to predict transpiration of citrus trees on

day-to-day basis for purposes such as irrigation scheduling. The use of the Penman-

Monteith equation coupled with a Jarvis-type canopy conductance to predict long-

term transpiration was evaluated in the three orchards. Bulk canopy conductance

was calculated from the measured transpiration using a top-down approach by

inverting the Penman-Monteith equation. Response functions for solar radiation,

temperature and vapour pressure deficit were parameterised for a Jarvis model

based on the measured data. The Jarvis model was first parameterized in the ‘Delta’

Valencia orchard. On validation the approach predicted transpiration in the same

orchard reasonably well. However, transpiration was overestimated in the

‘Bahianinha’ orchard and underestimated in the ‘Rustenburg’ Navel orchard when

the Jarvis parameters obtained in the ‘Delta’ Valencia orchard were applied to the

two orchards. When the Jarvis model was parameterized in the ‘Bahianinha’ and

‘Rustenburg’ Navel transpiration was predicted fairly well. A single set of response

functions for canopy conductance obtained in each orchard was found to be able to

accurately predict transpiration in the respective orchard for a fairly long period. This

approach may be applicable to sub-tropical conditions where wetting of the canopy

by rainfall and occurrence of cloudy/overcast conditions are both infrequent.


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Contents

Acknowledgements ..................................................................................................... i

Declaration .................................................................................................................. ii

Abstract ...................................................................................................................... iii

List of Figures ............................................................................................................. x

List of Tables ............................................................................................................. xv

List of abbreviations and symbols ........................................................................... xvii

Introduction and structure of thesis ............................................................................ 1

Aim of the study ...................................................................................................... 7

Thesis objectives .................................................................................................... 7

Hypotheses ............................................................................................................. 7

Thesis outline ......................................................................................................... 7

Chapter 1: Literature Review ...................................................................................... 9

1.1 Measurement of citrus water use ......................................................................... 9

1.1.1 Introduction .................................................................................................... 9

1.1.2 Sap flow measurements of crop water use .................................................. 13

1.1.2.1 Theory of heat pulse sap flow technique ............................................... 14

1.1.2.2 Compensation heat pulse method ......................................................... 15

1.1.2.3 Heat ratio method .................................................................................. 16

1.1.2.4 Correction for wounding ........................................................................ 17

1.1.2.5 Calibration of the heat pulse techniques ............................................... 18

1.1.2.6 Scaling from sample trees to orchard level ........................................... 19

1.1.3 Micrometeorological estimates of evapotranspiration .................................. 20

1.1.3.1 Eddy covariance method ....................................................................... 20

1.1.3.1.1 Direct measurement ........................................................................... 21

1.1.3.1.2 Energy balance method ..................................................................... 21

1.2 Modelling citrus water use .................................................................................. 23

1.2.1 Introduction .................................................................................................. 23

1.2.2 Crop coefficient approach ............................................................................ 24

1.2.2.2 Single crop coefficient ........................................................................... 25

1.2.2.3 Dual crop coefficient .............................................................................. 25

1.2.2.4 Reference evapotranspiration ............................................................... 25

1.2.2.5 Citrus crop coefficients .......................................................................... 27


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1.2.3 Estimation of transpiration crop coefficients from fractional ground cover and

crop height ............................................................................................................ 31

1.2.3.1 Basal crop coefficient during peak plant growth (Kcb full) ........................ 32

1.2.3.2 Estimation of plant density coefficient (Kd) ............................................ 33

1.2.4 Modelling canopy conductance.................................................................... 36

1.2.4.1 Jarvis-type model .................................................................................. 37

1.2.4.3 Aerodynamic conductance .................................................................... 38

1.3 Scope of the study .............................................................................................. 39

Chapter 2: Calibration of the heat ratio method (HRM) sap flow technique for long-

term transpiration measurement in citrus orchards .................................................. 41

2.1 Introduction ........................................................................................................ 41

2.2 Materials and methods ....................................................................................... 43

2.2.1 Experimental Site and Climate ..................................................................... 43

2.2.2 Sap flow measurements .............................................................................. 44

2.2.2.1 Measurement of heat pulse velocities ................................................... 44

2.2.2.2 Wounding correction ............................................................................. 47

2.2.2.3 Determining sap velocity ....................................................................... 47

2.2.2.4 Converting sap velocity to sap flux density............................................ 49

2.2.2.5 Xylem anatomical assessments ............................................................ 50

2.2.3 Measurement of orchard evapotranspiration ............................................... 51

2.2.3.1 The eddy covariance system ................................................................. 51

2.2.4 Calibration of the HRM sap flow technique .................................................. 52

2.3 Results ............................................................................................................... 54

2.3.1 Calibration of the HRM sap flow technique .................................................. 54

2.3.3 Xylem anatomy ............................................................................................ 57

2.4 Discussion .......................................................................................................... 60

2.5 Conclusions ........................................................................................................ 62

Chapter 3: Measurement of long-term transpiration and transpiration coefficients in

citrus orchards .......................................................................................................... 63

3.1 Introduction ........................................................................................................ 63


3.2.1 Experimental site and climate ...................................................................... 64

3.2.2 Estimation of transpiration ........................................................................... 66

3.2.3 Reference evapotranspiration ...................................................................... 68


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3.2.4 Determination of transpiration (Kt) crop coefficients..................................... 69

3.3 Results and discussion ....................................................................................... 70

3.3.1 Measurement of long-term transpiration ...................................................... 70

3.3.2 Determination of transpiration crop coefficients (Kt)..................................... 74

3.4 Conclusions ........................................................................................................ 78

Chapter 4: Estimation of transpiration crop coefficients from ground cover and height

in citrus orchards ...................................................................................................... 80

4.1 Introduction ........................................................................................................ 80

4.2 Materials and Methods ....................................................................................... 81

4.2.1 Model description ......................................................................................... 81

4.2.2 Model calibration .......................................................................................... 83

4.2.3 Model validation ........................................................................................... 84

4.3 Results and discussion ....................................................................................... 84

4.4 Conclusions ........................................................................................................ 93

Chapter 5: Predicting transpiration of citrus orchards using the Penman-Monteith

equation coupled with a Jarvis-type multiplication canopy conductance model ....... 94

5.1 Introduction ........................................................................................................ 94


5.2.1 Calculation of canopy conductance ............................................................. 95

5.2.2 Modelling canopy conductance.................................................................... 96

5.2.2.1 Model parameterisation ......................................................................... 97

5.2.2.2 Model validation .................................................................................... 98

5.2.3 Statistical analysis ....................................................................................... 98

5.3 Results ............................................................................................................... 99

5.3.1 Canopy conductance ................................................................................... 99

5.3.2 Parameterisation of the Jarvis model ......................................................... 102

5.3.2 Predicting transpiration using the Penman-Monteith equation coupled with

the Jarvis-type model .......................................................................................... 104

5.4 Discussion ........................................................................................................ 117

5.5 Conclusion ....................................................................................................... 119

Chapter 6: General conclusions and recommendations ......................................... 120

6.1 Overview of study ............................................................................................. 120

6.2 Calibration of the heat ratio method (HRM) sap flow technique for long-term

transpiration measurement in citrus orchards ........................................................ 121


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6.3 Measurement of long-term transpiration and transpiration coefficients in citrus

orchards ................................................................................................................. 121

6.4 Estimation of transpiration coefficients from plant height and canopy cover .... 123

6.5 Predicting transpiration of citrus orchards using the Penman-Monteith equation

coupled with a Jarvis-type canopy conductance model.......................................... 123

6.6 Recommendations for future research ............................................................. 124

References ............................................................................................................. 126


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List of Figures

Figure 1. Citrus production according to province and type in South Africa in the

2014/15 growing season (Citrus Growers Association of Southern Africa,

2015a). .................................................................................................... 2

Figure 2. Quantity of oranges produced for local consumption, exports and

processing in South Africa (Source: Citrus Growers Association of

Southern Africa, 2015b). ......................................................................... 3

Figure 3. Gross values of oranges on the different markets in South Africa (Source:

Citrus Growers Association of Southern Africa, 2015b). ......................... 3

Figure 1.1 Schematic diagram of a probe set used for sap flow measurements

using the HRM showing the heater probe, upper (down-stream) and

lower (up-stream) temperature sensors. The depth of probe insertion d;

and the distance between the heater probe and both temperature

sensors x are also shown. ..................................................................... 17

Figure 1.2. Simplified representation of the (bulk) surface and aerodynamic

resistances for water flow through the soil-plant-atmosphere continuum

(Allen et al., 1998). ................................................................................ 24

Figure 1.3. Characteristics of the hypothetical reference crop used for calculation of

ETo in the FAO Penman-Monteith equation (Allen et al., 1998). ........... 26

Figure 2.1. Sap flow probes installed in two trees in the ‘Delta’ Valencia orchard.

Insert shows situation of the probes around a stem of one of the sample

trees. ..................................................................................................... 46

Figure 2.2. Sample of wood taken from one of the sample trees for the

determination of wounding width, sapwood moisture content and

sapwood density: (A) the sample of wood just before removal (B)

measurement of the wounding width and (C) the wood sample used for

measurements ...................................................................................... 48

Figure 2.3. Measurement of the wounding width on a wood sample cut transversely

from the trunk of one of the sample trees at the end of the measuring

season in August 2009 (photo courtesy of Mark Gush)......................... 48

Figure 2.4. Idealised cross-sectional areas of four annuli rings represented by probe

sets inserted at different depths in the conducting sapwood of a tree

stem shaded in different colours. .......................................................... 50


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Figure 2.5. Micro-meteorological instruments including mounted on a lattice mast at

the centre of the ‘Delta’ Valencia orchard (photo courtesy of Mark Gush).

.............................................................................................................. 53

Figure 2. 6. Error analysis illustrating resultant percentage error in transpiration from

the HRM due to errors in selected parameters in the up-scaling

equations from Vh’s to transpiration, whilst maintaining all other

parameters at their original value. ......................................................... 55

Figure 2.7. Comparison between daily transpiration obtained using a virtual wound

width of 3.3 mm for the winter period and 3.1 mm for the autumn period.

.............................................................................................................. 57

Figure 2.8. Up-scaled HRM-based transpiration using a “virtual wound width” of 3.2

mm as compared to micrometeorological measurements of

evapotranspiration. ................................................................................ 58

Figure 2.9. Photomicrographs of sapwood samples taken from a ‘Valencia’ orange

tree. (A) A transverse section of the citrus sapwood prior to probe

insertion showing the distribution of the xylem vessels (x) in the

sapwood; (B) a transverse section of sapwood adjacent to one of the

drilled holes made for insertion of a probe; (C) tangential section

adjacent to one of the drilled holes showing the affected rays; (D) a

transverse section showing the extent of blockage of xylem vessels by

gum (g) and phenols (p); and (E) a transverse section of the sapwood

approximately 1 mm above the downstream thermocouple showing

extensive xylem blockage. Scale bars on each photograph are equal to 2

mm. ....................................................................................................... 59

Figure 3.1. Relationship between trunk circumference and seasonal water use for

the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards ................................ 68

Figure 3.2. Daily transpiration and reference evapotranspiration determined in the

‘Delta’ Valencia, ‘Bahianinha’ and ‘Rustenburg’ Navel orchards. .......... 71

Figure 3.3. Transpiration coefficients (Kt) determined for the ‘Delta’ Valencia,

‘Bahianinha’ Navel and ‘Rustenburg’ Navel orchards............................ 75

Figure 3.4. Average monthly transpiration coefficients (Kt) for the three orchards.

Also shown are the FAO-56 standardised basal crop coefficients (Kcb

FAO-56) for a citrus orchard with 70 % canopy cover (‘Delta’ and


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‘Rustenburg’ orchards) and 50 % ground cover (‘Bahianinha’ orchard),

all with no active ground cover, as given by Allen and Pereira (2009). . 76

Figure 4.1. Derived monthly transpiration crop coefficients (Kt) for the three

orchards. Transpiration crop coefficients were determined using

measured transpiration (Kt measured), the method described in Allen and

Pereira (2009) using the parameters given for citrus (Kt Allen and Pereira),

using estimates of monthly average rl values from transpiration data (Kt

monthly avg. rl) and using rl estimated from the relationship with ETo (Kt

rl (ETo)). Also shown are FAO-56 standardised basal crop coefficients

(Kcb FAO-56) for a citrus orchard with 70% canopy cover (‘Delta’ and

‘Rustenburg’ orchards) and 50% ground cover (‘Bahianinha’ orchard), all

with no active ground cover, as given by Allen and Pereira (2009) ....... 85

Figure 4.2. Monthly mean leaf resistances calculated following the procedure

outlined by Allen and Pereira (2009), compared with the values

suggested by Allen and Pereira (2009) for citrus and daily stomatal

resistance measure in the ‘Rustenburg’ Navel orchard in Citrusdal. ..... 86

Figure 4.3. Relationship between reference evapotranspiration (ETo) and mean leaf

resistance for the ‘Rustenburg’ Navel orchard ...................................... 88

Figure 4.4. Monthly measured and estimated transpiration using Kt values derived

from mean leaf resistance, estimated from the relationship between

reference evapotranspiration and mean leaf resistance in the three

orchards. Statistical parameters shown include mean absolute error

(MAE), root of the mean square error (RMSE) and index of agreement

(D) ......................................................................................................... 89

Figure 4.5. Cumulative ETo, measured transpiration and transpiration estimated

from the derived crop coefficients in the ‘Delta’ Valencia orange orchard

(1 August 2008 to 30 July 2009), the ‘Bahianinha’ Navel orchard (3

September 2009 to 30 June 2010) and the ‘Rustenburg Navel orchard

(13 August 2010 to 12 August 2011) ..................................................... 92

Figure 5.1. Typical diurnal trend of A) solar radiation (SR), B) temperature (T), C)

vapour pressure deficit (VPD) and D) canopy conductance (gc),

calculated from the inversion of the Penman-Monteith, in the ‘Delta’

Valencia orchard on a clear sky day, 27 January 2010. ...................... 100


xiii

Figure 5.2. Hourly canopy conductance (gc) calculated using the measured

transpiration and inverting the Penman-Monteith equation in the three

orchards. Gaps in the plotted data were due to missing hourly weather

data caused by power failure to the weather stations.......................... 101

Figure 5.3. Normalised canopy conductance in the ‘Delta’ Valencia orchard plotted

against (A) solar radiation (B) vapour pressure deficit and (C)

temperature. The forms of the model functions, based upon the

optimised parameters, are shown as solid lines. ................................. 103

Figure 5.4. Relationship between hourly gc predicted by the Jarvis model and gc

obtained from sap flow data by inverting the Penman-Monteith equation

in the ‘Delta’ Valencia orchard. ............................................................ 104

Figure 5.5. Measured and predicted daily transpiration in the ‘Delta’ Valencia

orchard for A) the period 16 December 2008 to 26 June 2009 and (B)

regression analysis. Statistical parameters include slope of regression

equation, coefficient of determination (R2), mean absolute error (MAE),

Willmot coefficient of agreement (D) and root mean square error

(RMSE). The missing data was due to missing hourly weather data

caused by power failure to the weather station. .................................. 105

Figure 5.6. Relationship between gc predicted by the Jarvis model using parameters

of the ‘Delta’ Valencia orchard and gc obtained from sap flow data by

inverting the Penman-Monteith equation in the ‘Bahianinha’ and

‘Rustenburg’ Navel orchards. .............................................................. 107

Figure 5.7. Time series of measured and predicted transpiration in the ‘Bahianinha’

and ‘Rustenburg’ Navel orchards using Jarvis parameters optimised in

the ‘Delta’ Valencia orchard. ............................................................... 108

Figure 5.8. Regression analysis between measured and predicted transpiration in

the ‘Bahianinha’ and ‘Rustenburg’ Navel orchard using parameters

determined in the ‘Delta’ Valencia orchard. Statistical parameters used

include slope of regression equation, coefficient of determination (R2),

mean absolute error (MAE), Willmot coefficient of agreement (D) and

root mean square error (RMSE). ......................................................... 109

Figure 5.9. Normalised canopy conductance in the ‘Bahianinha’ Navel orchard

plotted against (A) solar radiation (B) vapour pressure deficit and (C)


xiv

temperature. The forms of the model functions based upon the optimised

parameters are shown as solid lines. .................................................. 111

Figure 5.10. Normalised canopy conductance in the ‘Rustenburg’ Navel orchard

plotted against (A) solar radiation, (B) vapour pressure deficit and (C)

temperature. The forms of the model functions based upon the optimised

parameters are shown as solid lines. .................................................. 112



in the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards. ......................... 113

Figure 5.12. Time series plot of measured and predicted transpiration in the

‘Bahianinha’ and ‘Rustenburg’ Navel orchards. The gaps in the plotted

data were due to missing hourly weather data caused by power failure to

the weather stations. ........................................................................... 114

Figure 5.13. Regression analysis between predicted and measured transpiration in

the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards. Statistical parameters

used include slope of regression equation, coefficient of determination

(R2), mean absolute error (MAE), Willmot coefficient of agreement (D)

and root mean square error (RMSE). .................................................. 115

Figure 5.14. Cumulative measured transpiration and transpiration predicted using a

Jarvis-type model parameterised in the respective orchards for the

measurement periods. The plateau in water use graphs occurring

around April/May in the three graphs is due to periods of missing data.

............................................................................................................ 116


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List of Tables

Table 1.1. Average annual and seasonal crop water use (mm day-1) of citrus tree

orchards, in different growing areas of the world. .................................. 10

Table 1.2. Citrus crop coefficient (Kc and Kcb) values for standard climate of RHmin =

45 % and u2 = 2 m s-1 as published for use with FAO Penman-Monteith

ETo (Allen et al. 1998). .......................................................................... 28

Table 1.3. Seasonal crop coefficients determined in citrus orchards across the

growing regions of the world. ................................................................ 30

Table 1.4. Generic parameters for a citrus crop for estimating crop coefficients. .... 35

Table 1.5. Citrus values of Kcini, Kc mid, Kc end, Kcbini, Kcb mid and Kcb end for standard

climate of RHmin = 45 % and u2 = 2 m s-1 as expanded from FAO-56

(Allen et al. 1998) for a range of values for effective ground covered by

the tree canopy (fc eff) during the midseason and using the procedure of

Allen and Pereira (2009) with recommended parameter values. ........... 35

Table 2.1. Established circumference size classes (CSC) established, the number

of trees in the class (n), the sample tree representing each class, sample

tree circumference (Sc) and the fraction represented by each sample

tree in the ‘Delta’ Valencia orchard as a percentage (pt). ...................... 45

Table 2.2. Sapwood water content and sapwood density for various citrus species. A

total of 19 samples were taken, with six from lemon, nine from sweet

orange, two from soft citrus and two from grapefruit. ............................ 55

Table 2.3. Slopes and intercepts of the regression equations used to determine

wounding width by inputting ETc on different days. The R2 values and the

virtual wound widths determined from the regression equations are also

shown. ................................................................................................... 56

Table 3.1. Established circumference size classes (CSC), the number of trees in the

class (N), the sample tree representing each class, sample tree

circumference (Sc) and the percentage represented by each sample tree

each orchard (Pt). .................................................................................. 67

Table 3.2. Average daily transpiration (T) and reference evapotranspiration (ETo) for

the summer and winter seasons in the ‘Delta’ Valencia and ‘Bahianinha’

Navel. .................................................................................................... 72


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Table 3.3. Average transpiration (T), reference evapotranspiration (ETo) and

transpiration crop coefficients (Kt) for the summer and winter seasons. 77

Table 5.1. Optimised parameters for the Jarvis model used to predict canopy

conductance with vapour pressure deficit, solar radiation and ambient

temperature as response functions in the ‘Delta’ Valencia orchard. .... 102

Table 5.2. Parameters for the response functions of vapour pressure deficit, solar

radiation and temperature for the Jarvis model determined through the

optimisation process in the ‘Bahianinha’ and ‘Rustenburg’ Navel

orchards. ............................................................................................. 110


xvii

List of abbreviations and symbols

Abbreviations

CHPM compensation heat pulse method

CSC circumference size classes

DWAF Department of Water Agriculture and Forestry

ETc orchard evapotranspiration

FAO Food and Agriculture Organization of the United Nations

HRM heat ratio method

IPCC Inter-Governmental Panel on Climate Change

IRGA open path infrared gas analyser

LAI leaf area index

MAE mean absolute error

OPEC open path eddy covariance

Sc sample tree circumference

TC thermocouple

Symbols

Symbol Description

Ab canopy basal area

AT total area allocated to each tree in the orchard

cw specific heat capacity of the wood matrix

cs specific heat capacity of the sap

d characteristic leaf dimension

ETc crop evapotranspiration

ETo reference evapotranspiration

ƒceff effective fraction of ground covered or shaded by vegetation

near solar noon

Fr adjustment factor relative to stomatal control

G Ground heat flux

gc canopy conductance

gc max maximum canopy conductance

h mean maximum plant height during the midseason period or

full cover period


xviii

k thermal diffusivity of green (fresh) wood

Kcb basal crop coefficient

Kcb full basal crop coefficients for fully grown orchard

Kc min minimum crop coefficient for bare soil

Kd crop density coefficient

Ke soil water evaporation coefficient

K canopy extinction coefficient of light attenuation

Mw wet mass of the sapwood sample

Md dry mass of the sapwood sample

ML parameter that simulates the physical limits imposed on water

flux through the plant root, stem and leaf systems

N number of sample trees on which transpiration was conducted

pti portion of trees represented by the ith tree sampled in the

orchard

Q sap flux

Rw inter-row spacing

Reff effective precipitation

RHmin minimum relative humidity

rk radii forming the annuli rings of the sap wood measured from

the centre of the trunk

rl mean leaf resistance

Rn net irradiance

Rn total net radiation flux density

SR solar radiation

RO run-off

rs estimated mean canopy bulk resistance for the citrus trees

T orchard transpiration

Ta mean daily air temperature at 2 m height

TL lower temperature limit to transpiration

TU upper temperature limit to transpiration

Tpost temperature measured after the heat pulse

Tpre average temperature before the heat pulse

u2 wind speed at 2 m height


xix

v1 increase in temperature of upper thermocouple after the heat

pulse is released

v2 increase in temperature of the lower thermocouple after the

heat pulse is released

Vc corrected heat pulse velocity

Vh heat pulse velocity

VPD vapour pressure deficit

Vs sap velocity

Vw volume of wood sample

W average or effective tree canopy width

w wounding width

Δ slope of the vapour pressure curve

δM function of soil water content deficit

ρb basic density of wood

ρs density of water

γ psychrometric constant


1

Introduction and structure of thesis

The genus Citrus (family Rutaceae) is a range of fruits which includes oranges,

mandarins, tangerines, tangelos, clementines, satsumas, lemons, limes, and

grapefruits (Syvertsen and Lloyd, 1994; Carr, 2012). Citrus are perennial evergreen

trees believed to have originated from the humid tropics of the south-eastern parts of

China and in southern India (Kriedemann and Barrs, 1981; Sippel, 2006). The

species have, however, become widely adapted to the semi-arid regions of the world

(Carr, 2012). They are cultivated primarily for fresh fruit and juice, although there are

other by-products, such as food additives, pectin, marmalades, cattle feeds (from the

peel), cosmetics, essential oils, chemicals, and medicines.

Citrus is a one of the most important fruit crops grown across the world, as well as in

South Africa. South Africa has an average production of 2.16 million tons per year,

which accounts for 4.2 % of world production and as a result the country is ranked

thirteenth in the world in terms of citrus production (FAO, 2012). In South Africa,

Valencia (including mid-seasons) and Navel orange orchards occupy the bulk of the

64 510 ha planted with citrus at the present moment, accounting for 40 and 24.3 %

of the total area planted to citrus, respectively (Citrus Growers Association of

Southern Africa, 2015a) (Figure 1). Figure 2 shows total orange production and the

quantity of fruit that was used for local consumption, processed and exported in

South Africa in recent years (Citrus Growers Association of Southern Africa, 2015b).

While the quantity of fruit used for local consumption and processing has remained

fairly constant over the years, there has been a gradual increase in the fruit sold on

the export market. This is probably due to the ever increasing price of fresh fruit on

the export markets (Figure 3) where South Africa is ranked third.

Citrus is grown in all provinces of South Africa with rare to frost-free conditions (this

excludes Gauteng and Free State) (Bijzet, 2006). The major producing provinces are

the Eastern Cape, Mpumalanga, Limpopo and Western Cape (Figure 1). A large

portion of these areas receive seasonal rainfall, less than 500 mm per annum,

making them semi-arid and therefore irrigation is required in order to meet crop

water requirements and enable the successful production of citrus in these areas.


2

Figure 1. Citrus production according to province and type in South Africa in the

2014/15 growing season (Citrus Growers Association of Southern Africa,

2015a).


3

Year

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

Qu

antity

of o

ran

ge

s (

t ye

ar-1

)

0.0

2.0e+5

4.0e+5

6.0e+5

8.0e+5

1.0e+6

1.2e+6

1.4e+6

1.6e+6

1.8e+6

2.0e+6

Total

Local

Export

Processed

Figure 2. Quantity of oranges produced for local consumption, exports and

processing in South Africa (Source: Citrus Growers Association of

Southern Africa, 2015b).

Year

2004 2006 2008 2010 2012 2014

Gro

ss v

alu

e o

f ora

nges (

Rands t

-1)

0

1000

2000

3000

4000

5000

6000

7000

Average

Exports

Processed

Figure 3. Gross values of oranges on the different markets in South Africa (Source:

Citrus Growers Association of Southern Africa, 2015b).


4

Currently, it is estimated that irrigated agriculture uses approximately 70 % of the

available fresh water resources on a global scale (FAO-AQUASTAT, 2003) and in

South Africa it is estimated at 60 % (DWAF, 2013). It has been predicted that as the

world population expands and economies grow, competition for water will increase,

while water resources become more polluted. These changes are expected to be

exacerbated as a result of climate change, which is believed to have already

increased the frequency and severity of droughts in southern Africa in recent years

(IPCC, 2007). Consequently, the demand for water will exceed supply, and less

water will be available for agriculture. These population and climate dynamics will

have catastrophic effects on 90 % of the fruit production industry in South Africa

which, according to Annandale et al. (2005), is entirely dependent on irrigation water.

Water-saving agricultural practices and sound water management strategies are

therefore urgently required to ensure the long-term sustainability of the industry.

The advent of precision irrigation systems, such as drip, provides an opportunity to

match crop water requirements and irrigation amounts, but needs to be coupled with

appropriate water management techniques (Jones, 2004). Insufficient knowledge of

fruit tree water use under these relatively new systems has been identified as a

major factor hindering the development of sound water management tools in South

Africa (Pavel et al., 2003; Volschenk et al., 2003). Available literature on citrus water

use measurements is in the form of Green and Moreshet (1979) and Du Plessis

(1985), which emphasizes that very little has been done in terms of research on

citrus water use in South Africa in recent years. There is need to update such

information to cater for changes in production practices.

Accurate and reliable methods of measuring water use in fruit tree orchards are

needed to gather information to fill this knowledge gap. Crop evapotranspiration

(ETc) can be measured using a number of systems which include lysimeters, micro-

meteorological methods, soil water balance, sap flow, scintillometry and satellite-

based remote sensing (Allen et al., 2011). Quantification of the transpiration

component that forms the larger portion of orchard water use (Reinders et al., 2010)

and is directly related to productivity (Villalobos et al., 2013), is critical in micro-

irrigated fruit tree orchards. Reviews by Swanson (1994), Smith and Allen (1996),

Wullschleger et al. (1998) and Allen et al. (2011) have reported sap flow


5

measurements as accurate and reliable methods for estimating long-term

transpiration of woody species such as citrus trees, provided the method is

calibrated and that due care is taken during installation of the equipment.

Measurements of crop water use are considered to be expensive and time

consuming, requiring specialised expertise, which is not always available. Physically-

based models can be used for the extrapolation of measured crop water use to

different environments for the improvement of irrigation water management (Boote et

al., 1996). The term irrigation water management used here encompasses the

activities of irrigation system planning, irrigation scheduling and issuing of water

rights/permits. According to Allen et al. (2011), ETc is typically modelled on a

physical basis using weather data and algorithms that describe the surface energy

and aerodynamic characteristics of the crop. Simultaneous measurements of ETc

and weather data are required to improve the current models; as well as adapt the

models to account for new production practices e.g. use micro-irrigation.

The crop coefficient approach first published by Doorenbos and Pruitt (1977), and

later refined by Allen et al. (1998), has been used extensively and is currently

considered as the standard model of ETc. Although site specific crop coefficients are

probably best, the crop coefficients for a generic citrus tree orchard are often used

for water management, due to a lack of reliable information on tree water use. The

basal crop coefficient (Kcb), which is directly linked to transpiration, is very important

in micro-irrigated orchards, as it represents the major component of orchard water

use and is directly linked to productivity (Villalobos et al., 2013). Villalobos et al.

(2013) highlighted that the Kcb factors published by Allen et al. (1998) contain some

residual diffusive evaporation component supplied by soil water below the dry

surface and by soil water from beneath dense vegetation; such that the term

transpiration coefficients (Kt) should be used when basal crop coefficients are

determined using transpiration determined by sap flow methods.

The crop coefficient approach is often used in irrigation water management because

it is relatively simple to implement. Research has shown much variation in crop

coefficients reported for citrus orchards across the different growing regions of the


6

world (García Petillo and Castel, 2007; Snyder and O’Connell, 2007). This means

that crop coefficients may be site specific and may not be readily transferable from

one orchard to another (Testi et al., 2006). Allen and Pereirra (2009) consolidated

the FAO56 procedure for estimating crop coefficients and developed a method for

developing site specific crop coefficients based on the fractional cover and height of

the vegetation and the degree of stomatal control over transpiration relative to most

agricultural crops. The use of this approach still needs to be tested against Kt

determined using sap flow measurements in citrus orchards.

Citrus trees have been associated with high resistances that play a major role in the

regulation of water movement within the plant (van Bavel et al. 1967; Kriedemann

and Bars, 1981; Meyer and Green, 1981; Sinclair and Allen, 1982). Sap flow-based

transpiration measurements have proved useful in the parameterisation of canopy

conductance models for different tree species including citrus (e.g. Rana et al., 2005;

Oguntunde et al., 2007; Villalobos et al., 2009; Villalobos et al., 2013). A canopy

conductance model, that has been evaluated for short periods, as in the case for the

studies for citrus cited above, is the multiplicative approach that was conceived by

Jarvis (1976). Besides aiding scientists in understanding the bulk behaviour of

stomatal conductance with respect to changing environmental conditions

(Wullschleger, 1998), it has also been incorporated into the Penman-Monteith

equation to estimate transpiration. The use of such a canopy conductance modelling

approach can play a vital role in mechanistically modelling transpiration of citrus

trees, where hydraulic conductance plays an important role in regulating

transpiration.

This study was part of a project solicited, initiated, managed and funded by South

Africa’s Water Research Commission (Project K5/1770) entitled “Water use of fruit

tree orchards” with core objectives of measuring and modelling of water use of

selected fruit tree orchards.


7

Aim of the study

The aim of this study was to measure transpiration of well managed micro-irrigated

citrus orchards and test physically–based models that can be used to estimate

transpiration across different citrus growing regions.

Thesis objectives

The objectives of the thesis were to:

1. Calibrate the heat ratio method (HRM) sap flow technique using micro-

meteorological measurements for long-term transpiration measurement in a

citrus orchard

2. Quantify long-term transpiration and transpiration crop coefficients in citrus

orchards using the calibrated sap flow technique

3. Evaluate the appropriateness of the canopy cover-based transpiration crop

coefficient approach as a method for estimating transpiration in citrus

orchards

4. Use sap flow-based transpiration measurements to parameterise a Jarvis-

type conductance model for inclusion in the Penman-Monteith model for

predicting long-term transpiration of citrus orchards

Hypotheses

The main hypotheses that were formulated and tested in this study were as follows:

Citrus sapwood matrix is not thermally homogeneous such that conversion of

measured heat pulse velocity to transpiration requires an empirical calibration

factor which will be constant for long-term measurements

A dynamic estimate of leaf (or canopy) resistance is needed to predict the

daily and seasonal changes of transpiration in citrus orchards

Thesis outline

A review of the current knowledge on the measurement of evapotranspiration in

citrus is initially presented in Chapter 1. The main body of the thesis consists of four

chapters. The first two chapters (2 and 3) cover the specifics of measurement of


8

water use in three citrus orchards. Chapter 2 covers the calibration of the heat ratio

method (HRM) using micrometeorological measurements for estimating sap flow for

transpiration measurements in a ‘Delta’ Valencia orchard. In Chapter 3 details of

measuring long term transpiration using the calibrated HRM in three citrus orchards

are presented. Transpiration coefficients were determined for the three orchards

based on measured transpiration data and reference evapotranspiration determined

using the FAO56 Penman-Monteith equation. Physically-based models that can be

used for predicting transpiration of citrus orchards were tested in Chapters 4 and 5.

In Chapter 4, crop coefficients determined from measurements of canopy cover and

tree height, following the method of Allen and Pereira (2009), were evaluated against

those calculated based on measured transpiration and reference evapotranspiration

data. In Chapter 5, a mechanistic approach of modelling long-term citrus

transpiration using the Penman-Monteith equation coupled with a Jarvis-type canopy

conductance model was tested. Chapter 6 gives the general conclusions reached in

this work and some recommendations for future studies in relation to measurement

and modelling transpiration in citrus orchards.


9

Chapter 1: Literature Review

1.1 Measurement of citrus water use

1.1.1 Introduction

Knowledge of crop evapotranspiration (ETc) is the fundamental basis for efficient

irrigation water management strategies. The term irrigation water management

encompasses activities such as irrigation systems planning, irrigation scheduling and

issuing of water rights/permits. Besides irrigation water management knowledge of

crop evapotranspiration is also used across various disciplines as explained by Allen

et al. (2011) “crop ETc information is more and more frequently used as a foundation

for court determinations of injury among water users, for parameterization of

important hydrologic and water resources planning and operation models, for

operating weather and climate change forecasting models, and for water

management and allocation in water-scarce regions, including the partitioning of

water resources among states and nations”.

A great deal of research has been published on the water relations of Citrus spp.

Several reviews that synthesize this information have been published, which include

photosynthesis (Ribeiro and Machado, 2007), physiological aspects of the control of

the water status (Jones, 1985), irrigation (Shalhevet and Levy, 1990), physiological

responses to the environment (Syvertsen and Lloyd, 1994) and general water use

(Kriedemann and Barrs, 1981; Carr, 2012). Published data for ETc of Citrus species

across the different growing regions of the world is presented in Table 1.1. According

to these studies, citrus water use ranges from 0.8-8.5 mm day-1. Variation of crop

water use in citrus orchards can be attributed to a number of factors that include

varieties grown, rootstock, tree spacing, canopy height, ground cover, tillage,

microclimate, irrigation method and frequency; and method of measuring crop water

use (Snyder and O’Connell, 2006; Naor et al., 2008).


10

Table 1.1. Average annual and seasonal crop water use (mm day-1) of citrus tree orchards, in different growing areas of the world.

Reference Location Tec. CM Winter Spring Summer Autumn Annual Age spha

Koo and Sites (1955)* Florida, USA SWB ETc 1.7 2.7 4.0 2.8 2.8

Kalma and Stanhill (1969)* (Shamouti oranges)

Israel SWB ETc 1.1 4.4 2.3

Green and Moreshet (1979) (Valencia oranges)

South Africa Lys ETc 2.7 2.2 4.6 5.2 3.68 15

Hoffman et al. (1982) (Oranges)

Arizona, USA SWB ETc 1.1 4.0 7.3 3.7 4.0

Smajstrla et al. (1982) Florida, USA SWB ETc 1.9 3.9

Wiegand and Swanson (1982) (Valencia oranges)

Texas, USA SWB ETc 1.8 2.6 4.8 3.7 3.2

Rogers et al. (1983) Florida, USA SWB ETc 5 3.3 8

Du Plessis (1985) (Valencia oranges)

South Africa Lys ETc 2.3 6.0-8.5

Castel et al. (1987)* (Oranges)

Valencia, Spain SWB ETc 0.9-1.0 1.5-2.0 3.0-3.2 1.4-1.8 1.7-2.0

Sepaskhah and Kashefipour (1995)* (Lemons)

Iran SWB ETc 1.4 4.4 8.5 4.2 4.6

Castel (1997) (Clementines)

Spain Lys ETc 0.5 1.5 1 7-11 432

Fares and Alva (1999) (Hamlin oranges)

Florida,USA SWB ETc <1.0 >4.0

*Water use figures obtained from other sources and not the original reference Tec – technology used to measure water use: Lys – lysimeter; SWB – soil water balance; SF – sap flow; SR – surface renewal; EC – eddy covariance; μLys – microlysimeter CM – component of crop evapotranspiration that was measured: ETc –crop evapotranspiration; T – transpiration; Es – soil evaporation spha – stems per hectare (i.e. number of trees per hectare); Table 1.1 continued


11

Reference Location Tec. CM Winter Spring Summer Autumn Year Age spha

Castel (2000) (Clementines)

Valencia, Spain Lys ETc 0.7-1.0 2.0-2.8 1.9

Yang et al. (2003) (Murcott oranges)

Japan, Greenhouse

Lys ETc 0.6 5 4.4 8 4444

Rana et al. (2005) (Clementines)

Italy SF T 3 8 4 10 400

Consoli et al. (2006) (Navel oranges)

California, USA SR ETc 0.7mm h-

1 July-

August 4 337

0.8mm h-

1 15 299

0.9mm h-

1 34-

36 284

Alarcon et al. (2006) (Lemons)

Spain SF

T 1.8L day-

1 1.4 L day-1 2

García Petillo and Castel (2007) (Valencia oranges)

San Jose, Uruguay

SWB ETc 1.3 2.8 3.0 1.1 2.1

Snyder and O’Connell (2007) (Navel oranges)

Linsay, California SR ETc 2.36 3.86 5.55 4.7 4.14 33-37

283

Villalobos et al (2009) (Clementina mandarin)

EC μLys

T Es

1.3 0.82

1.8 0.82

17 333

Marin and Angelocci (2011) (Lemons)

Sao Paulo, Brazil SF T 0.8 2 7 179

ETc 0.8 2.7

Villallobos et al. (2013) (Navel oranges)

Southern Spain SF T 1.3 2.3 11 476

0.7 1.5 10 416


12

Table 1.1 also shows that the soil water balance has been used quite extensively to

measure ETc (and/or its components) of citrus. Other methods that have been used

for determining citrus ETc and/or its components include the micro-meteorological

methods (eddy covariance), lysimeters, and sap flow. Carr (2012) and García Petillo

and Castel (2007) highlighted that it is not easy to quantify the water requirements of

an orchard crop such as citrus or to compare the results of measurements taken

under different conditions and with different methods. Generally ETc measurements

are considered to be expensive, time consuming and requiring specialised expertise

(Allen et al., 2011). The situation is made worse in fruit tree orchards due to the

variability of tree sizes and the perennial nature of the crop, which means long time

periods are required to gather such information (Hoffman et al., 1982; Castel et al.,

1987).

Such dynamics may have had an effect on research of ETc of fruit trees in South

Africa, where such information is considered lacking (Pavel et al., 2003; Volschenk

et al., 2003). Research work from South Africa cited in Table 1.1 and in other

reviews (e.g. Carr, 2012; García Petillo and Castel, 2007) pertaining to citrus water

use was performed over three decades ago. There is need to update such

information to cater for changes in production practices such as rootstock choice

(from the more vigorous ‘Rough Lemon’ to the rootstocks of intermediate vigour

which include ‘Carrizo’, ‘Troyer’ and ‘Swingle’); and adoption of micro-irrigation

systems.

The use of micro-irrigation systems helps to maximise transpiration (i.e. beneficial

water use) and minimise evaporation (i.e. non-beneficial water use) in farming

systems (Reinders et al., 2010). It is important that ETc measurements in micro-

irrigated orchards focus on the transpiration component as it represents the major

component of ETc and is directly linked to productivity (Villalobos et al., 2013).

Thermometric sap flow techniques have shown great promise as methods for

measuring transpiration of woody tree species such as citrus (Smith and Allen, 1996;

Wullschleger et al., 1998). Sap flow methods have recently been used to quantify

transpiration of citrus orchards on a long-term basis by Marin and Angelocci (2011)

and Villallobos et al. (2013). Such methodologies can be utilised to expedite the

gathering of information on transpiration of citrus orchards in South Africa.


13

The next section reviews thermometric sap flow methods of measuring transpiration

in woody species. Emphasis is placed on the operational aspects that need to be

considered when quantifying long-term transpiration in orchards.

1.1.2 Sap flow measurements of crop water use

A number of methods have been used to directly estimate transpiration of trees in

general, including fruit trees (Wullschleger et al., 1998). These include weighing

lysimeters, large tree potometers, ventilated chambers, radioisotopes, stable

isotopes and a range of heat balance/heat dissipation methods. The most accurate

and accepted method is the weighing lysimeter and as such it has been used in a

number of studies in orchards (Moreshet and Green, 1984; du Plessis, 1985; Castel,

1996; Girona et al., 2002; Ayars et al., 2003; Girona et al., 2003; Yang et al., 2003;

Williams and Ayars, 2005). However, they are expensive to install in existing

orchards, as well as to maintain.

Amongst the several methods that have been used to measure tree transpiration, the

use of thermometric sap flow measurements has shown considerable promise

(Smith and Allen, 1996; Wullschleger et al., 1998; Allen et al., 2011). Sap flow

measurements at stem level can be used to estimate tree transpiration if performed

over sufficiently long periods to negate changes in stem storage and neglecting the

2-5 % of the water used for photosynthesis (Salisbury and Ross, 1978; Waring and

Roberts, 1978). Some of the advantages of these methods include their ability to

estimate transpiration, which has a direct relationship with productivity; easy

interface to data loggers for direct automated transpiration measurements; their

applicability is not inhibited by complex terrain and heterogeneity within fruit tree

orchards; and they exhibit relatively good accuracy when compared to conventional

methods of measuring orchard water use, e.g. the eddy covariance method (Rana et

al., 2005).

Thermometric techniques that have been used for transpiration measurements in

woody species can be broadly categorized into heat pulse, heat balance and heat

dissipation methods (Smith and Allen, 1996). Heat pulse techniques, particularly the

compensation heat pulse method (CHPM), have been widely used, mainly because


14

they are relatively easy to use and have low power requirements (Green et al., 2003;

Edwards et al., 1997; Smith and Allen, 1996). However, there are limitations to the

CHPM, of which the major shortcoming is the inability to measure low and reverse

sap flow rates, which usually occur under water stress conditions or at night (Becker,

1998). Burgess et al. (2001) developed the heat ratio method (HRM) as an

improvement to the CHPM, in order to cater for low and reverse sap flow rates in

woody species. The HRM has been used to study transpiration dynamics in Jatropha

curcas L. (Gush, 2008), olive (Williams et al., 2004; Er-Raki et al., 2010), Eucalyptus

marginata (Bleby et al., 2004) and Prosopis (Dzikiti et al., 2013).

1.1.2.1 Theory of heat pulse sap flow technique

The idea of using heat as a tracer of sap flow in woody tree species has been

perfected by several scientists over the years (Swanson, 1994). Marshall (1958)

further developed the theoretical framework used for heat pulse techniques, based

on a set of analytical solutions to the following heat flow equation:

𝜌𝑤𝑐𝑤𝑑𝑇

𝑑𝑡=

𝑑

𝑑𝑥𝜆𝑥

𝑑𝑇

𝑑𝑥+

𝑑

𝑑𝑦𝜆𝑦 − 𝑎𝑢𝜌𝑠𝑐𝑠

𝑑𝑇

𝑑𝑥+ 𝑄 Equation 1.1

where dT is the temperature departure from ambient (K) over an axial distance dx ,

dt is an increment in time (s), λ is the thermal conductivity (W m-1 K-1) in the axial (x)

and tangential (y) directions, a is the fraction of xylem cross sectional area occupied

by sap streams moving with a velocity u in the x-direction, and Q is the amount of

internal heat flux per unit length that is released from the heater (W m-3). Equation

1.1 ideally represents the two dimensional pattern of temperature surrounding a line

heater of zero dimension that is inserted into a section of sapwood of uniform

physical and thermal properties.

The velocity of the heat pulse carried by the moving sap stream is used to estimate

the rate of sap flow. Following the application of a heat pulse, the temperature rise in

the sapwood (Ts) at a distance from the heater is given by Marshall (1958) as:

𝑇𝑠 =𝑄

4𝜋𝜅𝑡𝑒𝑥𝑝 [

(𝑥−𝑉ℎ)+𝑦2

4𝜅𝑡] Equation 1. 2


15

where κ is the thermal diffusivity (m2 s-1) of the sapwood, t is time since the heat

pulse was applied, (x,y) is the point in the xylem at which temperature

measurements are made at time t and Vh is the heat pulse velocity.

Measurements of Vh are effected by inserting a line heater and a set of temperature

sensors into the sapwood of the species to be measured. In order to ensure that the

heater and temperature sensors are correctly aligned a guide jig is normally used

when drilling the holes. At least four probes consisting of the heater probe and

temperature sensors are required to capture the radial variations of sap flow rates in

the sapwood (Hatton et al., 1990). The method is suitable only for use on woody

stems of at least 30 mm in diameter that can accommodate the probes (Smith and

Allen, 1996). Its use is also limited in large stems where the entire sapwood cannot

be accessed.

1.1.2.2 Compensation heat pulse method

Of the heat pulse techniques the CHPM has been the most widely used (Goodwin et

al., 2006; Edwards et al., 1996). In the CHPM a heater probe is inserted radially into

the sapwood portion of the stem together with two temperature sensors located up-

and down-stream of the heater probe (commonly –5 and 10 mm, respectively). To

monitor the sap velocity, wood and sap are heated in pulses and heat is carried

through convection by the moving sap stream. When both temperature sensors have

warmed to the same temperature, the heat pulse would have moved to the midpoint

between the probes. The heat pulse velocity (Vh) is calculated from the time taken

for the heat pulse to cover this distance as follows:

𝑉ℎ =𝑥1+𝑥2

2𝑡0× 3600 Equation 1.3

where to is time (s) for the downstream and upstream temperature probes to reach

thermal equilibrium after the heat pulse has been released; and x1 and x2 denote

distance in mm between the heater and the downstream and upstream temperature

probes respectively. A negative value is assigned to x2 because it is located on the

opposite side of the heater to x1.


16

The principle used for measuring Vh in the CHPM has been found to overestimate

low, zero and reverse sap flow rates (Becker, 1998). This is because when sap flow

rates are low, the heat pulse may dissipate by conduction before it reaches the

measurement point, such that the sensors record equal temperatures (Burgess et

al., 2001). Lower thresholds for measurement of Vh depend on the sensitivity of

temperature sensors to capture the temperature changes, as well as the rate of

thermal diffusivity in xylem. Various lower limits that are undistinguishable from zero

have been reported e.g. 94 - 157 mm h–1 by Barrett et al. (1995); 36 - 72 mm h–1 by

Becker (1998); 40 mm h–1 by Burgess et al. (1998) and 30 mm h–1 by Swanson and

Whitfield (1981). Measured peak Vh in most woody species is seldom greater than

350 - 450 mm h–1, with mean rates less than half this value (Burgess et al., 2001).

Consequently, an inability of the CHPM to measure Vh below 30 - 40 mm h–1 will

affect the lower 10 - 30% of measurements. Measurements of transpiration during

winter, at night (Benyon, 1999) or on cloudy days are likely to be most affected. Such

erroneous measurements would have an impact on the long-term transpiration of

citrus which is known to have low conductance to water uptake.

1.1.2.3 Heat ratio method

Burgess et al. (2001) developed the HRM as an improvement to the CHPM to cater

for low and reverse sap flow rates in woody species. In the HRM, the ratio of the

increase in temperature is measured at points equidistant from a central heater soon

after a heat pulse is released. Heat pulse velocity (Vh) is calculated as:

2

13600v

vln

x

kVh Equation 1.4

where k is thermal diffusivity of green (fresh) wood (assigned a nominal value of 2.5

x 10-3 cm2 s-1), x is distance (cm) between the heater and either temperature probe,

and v1 and v2 are increases in temperature (from initial temperatures) at equidistant

points downstream and upstream (x cm) from the heater (Figure 1.1). During

operation temperature increases are measured and v1/v2 ratios are recorded

between 60 and 100 s after the release of the heat pulse. Vh are calculated based on

the average of the ratios during a measurement occasion of approximately 40 s.

Burgess et al. (1998; 2000) noted that there was a lesser occurrence of unexplained

variations of Vh data measured using the HRM as compared to CHPM equivalents

due to this improvement in sampling of measurements.


17

Figure 1.1 Schematic diagram of a probe set used for sap flow measurements

using the HRM showing the heater probe, upper (down-stream) and

lower (up-stream) temperature sensors. The depth of probe insertion d;

and the distance between the heater probe and both temperature

sensors x are also shown.

1.1.2.4 Correction for wounding

Heat pulse techniques are invasive in nature because the probes are inserted in the

sapwood and they therefore require correction of measured Vh to account for the

damage caused by drilling and constant heating, as well as the influence on heat

transfer of the materials used to construct the temperature sensor (Green and

Clothier, 1988; Fernández et al., 2006; Steppe et al., 2010). For the CHPM the

correction can be made using empirical models derived by Swanson and Whitfield

(1981) and Green and Clothier (1988) for a variety of temperature sensors spacings

and materials used to construct the heater probes and temperature sensors. The

models are of the following form:

𝑉𝑐 = 𝑎 + 𝑏𝑉ℎ + 𝑐𝑉ℎ2 Equation 1.5

where Vc is corrected heat pulse velocity, and a, b and c are coefficients calculated

by the models for various wound widths. The models used to estimate these

Bark + Cambium Centre of stem Heartwood

Sapwood

Sap flow

Heater Probe

d

Temperature

Sensors


18

coefficients as derived by Swanson and Whitfield (1981) and/or Green and Clothier

(1988) cannot be solved at zero sap flow and; that only compounds the problem of

poor resolution at low sap velocities using this method (Closs, 1958; Marshall, 1958;

Barrett et al., 1995).

Burgess et al. (2001) developed models for wound correction of the following form:

𝑉𝑐 = 𝑏𝑉ℎ + 𝑐𝑉ℎ2 + 𝑑𝑉ℎ

3 Equation 1.6

where b, c and d are coefficients calculated by the models for various wound widths.

The models developed by Burgess et al. (2001) for wounding correction to be used

in conjunction with the HRM are theoretically capable of estimating zero sap flow.

1.1.2.5 Calibration of the heat pulse techniques

Calibration of the heat pulse techniques is necessary for species with wood that are

not thermally homogeneous (Smith and Allen, 1996). Thermally homogeneous

sapwood should have both average xylem vessel lumen diameter and average

distance between the xylem vessels of less than 0.4 mm (Swanson, 1983). Sap flow

methods have been calibrated against other established methods to determine

adjustment coefficients (Green and Clothier, 1988; Steppe et al., 2010). These

established methods include weighing lysimeters (Caspari et al., 1993; Nortes et al.,

2008), whole tree gas exchange systems (Dragoni et al., 2005; Pernice et al., 2009),

cut tree experiments (Green and Clothier, 1988; Hatton et al., 1995; Fernández et

al., 2001), stem perfusion experiments (Green and Clothier, 1988; Fernández et al.

2006; Steppe et al., 2010) and micrometeorological measurements (Kostner et al.,

1992; Williams et al., 2004; Conceição and Ferreira, 2008; Poblete-Echeverría et al.,

2012).

Of all the parameters required to convert Vh to transpiration the wound width (i.e. the

damage caused by drilling and constant pulse heating) is difficult to estimate using

experimental procedures. A number of calibrations have shown that once all other

parameters have been experimentally determined, an apparent wound width can be

used to convert Vh measurements to transpiration in sapwood that is not thermally

homogeneous (Green and Clothier 1988; Zreik et al., 2003; Fernández et al., 2006).

Fernandez et al. (2006) termed this apparent wound width that could be used to


19

convert Vh’s to transpiration so that it matched transpiration measure with an

independent method a “virtual wound width”.

There seem to be contradicting views on the development of the wound width when

heat pulse techniques are used for long-term transpiration measurements. Early

research findings reported that wounding effects increase with time and

recommended that Vh probes should be moved regularly, either to a different part of

the same stem or to a new stem (Swanson and Whitfield, 1981; Marshall et al.,

1981; Smith and Allen, 1996; Zreik et al., 2003). To the contrary other authors

showed that only limited changes occurred in xylem properties during a long period

of Vh measurements in olive trees (Fernández et al., 2001; Giorio and Giorio, 2003;

Pernice et al., 2009). Dragoni et al. (2005) also suggested that a single calibration

was sufficient for long-term transpiration measurements in an apple orchard.

1.1.2.6 Scaling from sample trees to orchard level

In orchard situations sap flow measurements are normally conducted on a few

representative trees from which whole stand transpiration is then extrapolated. The

scaling of transpiration from sample trees to stand level can be based on leaf area

(Jara et al., 1998), variability of plant stem diameter (Daamen et al., 1999; Bethenod

et al., 2000) or plant density (Dugas and Mayeux Jr, 1991; Dragoni et al., 2005).

Irrigated fruit tree orchards constitute clonal trees that are genetically identical and

are normally trained similarly. The trees are mostly the same size, receive almost

equal amounts of radiant energy and receive equal amounts of water from a uniform

irrigation system. Little variation in transpiration of individual trees is expected (Smith

and Allen, 1996) such that stand transpiration can be estimated from the sample

trees using planting density (e.g. Dragoni et al., 2005). Use of allometric

relationships between sap flow of sample trees growth parameters (i.e. stem

diameter, stem basal area, sapwood area or leaf area) (e.g. Allen and Grime, 1995;

Soegaard and Boegh, 1995; Vertessy et al., 1995) may not hold true since the

canopies are manipulated. However, in studies of Cohen et al. (2008) and

Conceição and Ferreira (2008) transpiration of sample trees was successfully scaled

to whole stand transpiration as a weighted mean based on stem diameter of the

sample trees in the orchards.


20

1.1.3 Micrometeorological estimates of evapotranspiration

The EC is one micrometeorological method that is normally deployed into the

equilibrium boundary layer of a cropped area to estimate ETc (Allen et al., 2011).

Micrometeorological methods require large flat fields for the establishment of fetch

and minimum equipment height equipment to produce representative data (Paw et

al., 1995). Generally, instrumentation used for micrometeorological methods is

relatively fragile and expensive, such that constant technical attention is required;

and hence they are usually deployed into the field for short periods of time.

1.1.3.1 Eddy covariance method

Eddy covariance systems have been widely used to estimate ETc in orchards e.g.

olive (Testi et al., 2004; Villalobos et al., 2000; Pernice et al., 2009), apple (Jones et

al., 1988), pecan (Samani et al., 2011), mango (Teixeira and Bastiaanssen, 2012)

and citrus (Rana et al., 2005; Villalobos et al., 2009; Consoli et al., 2006) orchards.

The theory behind these measurements is based on the principle that turbulence in

the atmospheric boundary layer dominates mixing and the diffusion of sensible and

latent heat to and from the underlying surface (Swinbank, 1951). This requires high

speed measurement of sonic temperature, wind velocity, and water vapour pressure

or specific humidity, usually at frequencies of 5–20 Hz, using quick response

sensors. ETc is measured based on the high frequency of the turbulent ‘eddy flux’

motions in the surface boundary using the following statistical relationship of

Swinbank (1951):

𝐸𝑇𝑐 = 𝜌𝑎𝑤′𝑞′ =0.622

𝑝𝑤′𝑒′ Equation 1. 7

where ρa is density of moist air, p is atmospheric pressure, q’ is the instantaneous

deviation of specific humidity from mean specific humidity, e’ is the instantaneous

deviation of vapour pressure from mean vapour pressure, and w’ is the

instantaneous deviation of vertical wind velocity from mean vertical wind velocity.

The over-bar signifies a time average over a specified interval of time and the prime

indicates a departure from the mean. Sensors must measure vertical wind speed,

sonic temperature and humidity with sufficient frequency response to record the


21

most rapid fluctuations important to the diffusion process. Wind speed and humidity

sensors should be installed close to each other but separated sufficiently to avoid

interference because if the separation is too large, an underestimate of the flux may

result (Lee and Black, 1994). Many corrections are applied to arrive at the actual flux

measurements.

The wide use of the EC method has been attributed to a number of reasons which

include: relatively easy to setup, reduced cost of sensors and the ability to co-

measure energy balance components (as well as carbon dioxide fluxes depending

on equipment configuration) (Allen et al., 2011). ETc measurements based on the EC

method can be done using a direct measurement or calculated as a residual in the

shortened energy balance.

1.1.3.1.1 Direct measurement

Instrumentation for direct measurement of water fluxes using the EC method

involves the use of sonic anemometers and rapid-response open-path infra-red gas

analysers (Tanner, 1988; Tanner et al. 1993; Wilson et al., 2002; Baldocchi, 2003;

Shaw and Snyder, 2003; Meyers and Baldocchi, 2005). Using these instruments

fluxes of latent (λETc) and sensible heat (H) are measured with a high level of

precision and with a high degree of spatial and temporal resolution averaging 15-30

minute periods. Typically, a frequency of the order of 5–10 Hz is used, but the

response-time requirement depends on wind speed, atmospheric stability and the

height of the instrumentation above the surface.

1.1.3.1.2 Energy balance method

ETc can be calculated as a residual of the energy balance once the measurement of

other components of the energy balance has been determined. The shortened

energy balance equation can be written as follows:

𝜆𝐸𝑇𝑐 = 𝑅𝑛 − 𝐺 − 𝐻 Equation 1.8

where λETc is the latent heat flux, Rn is the net radiation, G is the heat flux transfer

into the soil, H is the sensible heat flux density. All terms have units of W m-2. Rn is


22

measured using net radiometers and G is measured using soil heat flux plates. The

sensible heat flux is measured using the EC method based on the following

statistical relationship of Swinbank (1951):

𝐻 = 𝜌𝑎𝐶𝑝𝑤′𝑇′ Equation 1.9

where T’ is the instantaneous deviation of air temperature from mean temperature

and Cp is specific heat of moist air. The use of the shortened energy balance has an

advantage of eliminating the requirement for the quick response hygrometer, which

can be expensive and can create high frequency fallout caused by physical

separation of the hygrometer from the sonic anemometer. The disadvantage of

estimating ETc as a residual of the shortened energy balance is the need to measure

Rn and G accurately, which can be problematic under conditions with sparse or

heterogeneous vegetation such as fruit tree orchards (Burba and Anderson, 2008). It

is also assumed that other terms of the full energy balance such as canopy stored

heat flux, advection flux e.t.c are negligible.

There are several corrections that must be applied to measurements because

practical instrumentation cannot fully meet the requirements of the underlying

micrometeorological theory (Foken et al., 2012). Typically, measurements are made

in a finite sampling volume rather than at a single point, and the maximum frequency

response of the sensors is less than the highest frequencies of the turbulent eddies

responsible for the heat and mass transport. Both of these cause a loss of the high-

frequency component of the covariances used to calculate fluxes. Errors also arise in

calculating fluxes of trace gas quantities using open-path analyzers because of

spurious density fluctuations arising from the fluxes of heat and water vapour. The

several corrections required on the sampled high frequency data for the EC method

to ensure that quality data are done using software such as EdiRe (Mauder et al.,

2008).

When the shortened energy balance is used it also must be checked for energy

balance closure error (Allen et al., 2011).This error occurs when the sum of

measured λETc + H does not equal measured Rn – G and can be in the range of 10

to 30 % for field experiments (Aubinet et al. 2000; Wilson et al. 2002). Foken et al.

(2008) listed the following as the possible causes for lack of closure (i) different


23

reference levels and different sampling scales of the measuring methods for net

radiation, turbulent fluxes, and soil heat flux (ii) heterogeneous landscape in the

vicinity of a flux-measurement site that is capable of generating eddies at larger time

scales, that can be detected by the EC method (iii) advection and fluxes associated

with longer wavelengths, and (iv) measurement errors. Energy balance closure is

usually achieved by scaling λETc and H in the same proportion (Twine et al., 2000)

or using multiple linear regression equations (Allen et al., 2008).

1.2 Modelling citrus water use

1.2.1 Introduction

Variability in measured ETc of citrus orchards means that these measurements

cannot be directly applied to all areas in which the crop is cultivated and under all

management practices. In addition measurements of ETc are expensive, time

consuming and requires specialised expertise which is not always available. Models

play a pivotal role in extrapolating these measurements to regions in which they

were not conducted. ETc is modelled on a physical basis using weather data and

algorithms that describe the crop’s surface and aerodynamic resistances (Allen et

al., 1998). According to Allen et al. (1998) the Penman-Monteith equation has been

used quite extensively. The form of the equation is as follows:

𝜆𝐸𝑇𝑐 =∆(𝑅𝑛−𝐺)+𝜌𝐶𝑝

𝑉𝑃𝐷

𝑟𝑎

∆+𝛾(1+𝑟𝑠𝑟𝑎

) Equation 1.10

where λETc is the evapotranspiration rate per unit leaf area (W m-2), Rn is the net

radiation flux density absorbed by the leaf (W m-2), ρ and Cp, are the density (kg m-3)

and specific heat capacity (J kg-1 K-1) of air at constant pressure, λ is the latent heat

of vaporisation of water (J g-1), γ is the psychrometric constant (kPa oC), Δ is the

slope of the water vapour pressure curve (kPa oC) at ambient air temperature Ta

(oC), VPD is the saturation vapour pressure deficit of the air (kPa), ra is the

aerodynamic resistance (s m-l), and rs is the bulk surface resistance (s m-1).

The rs and ra terms used to simplify the exchange process in a vegetation layer in

Equation 1.10, are crop specific and cannot be determined easily (Figure 1.2). The rs


24

term is used to describe the resistance of water flow through the soil-plant-

atmosphere continuum. The rs term combines resistances through the plant system

and ra describes the resistance from the surface of the vegetation upward and

involves friction from air flowing over vegetation surfaces (Figure 1.2). In order to

obviate the need to estimate the resistances parameters for each crop at different

stages of growth, the crop coefficient approach was introduced.

Figure 1.2. Simplified representation of the (bulk) surface and aerodynamic

resistances for water flow through the soil-plant-atmosphere continuum

(Allen et al., 1998).

1.2.2 Crop coefficient approach

The crop coefficient approach that was first published by Doorenbos and Pruitt

(1977) and later refined by Allen et al. (1998) has been used quite extensively in

modelling ETc, such that it is considered a standard for estimating ETc. ETc under

standard conditions is calculated as a product of experimentally determined crop

coefficients (Kc) and reference evapotranspiration (ETo). Standard conditions imply

that the crops are disease free, well fertilised, growing in large fields, under optimum

soil water conditions, and achieving full production under the given climatic

conditions. The method has been accepted in the field of irrigation water

management because it is relatively simple to use. The technical advantage of the

crop coefficient approach is that it makes it possible to consider the independent


25

contributions of evaporation and transpiration (Allen et al., 1998). This is done by

splitting the Kc factor into two separate coefficients namely soil evaporation

coefficient (Ke) and a basal crop coefficient (Kcb).

1.2.2.2 Single crop coefficient

In the single crop coefficient approach, the individual contributions of transpiration

and evaporation are combined to determine ETc as follows:

𝐸𝑇𝑐 = 𝐾𝑐 × 𝐸𝑇𝑜 Equation 1.11

The Kc coefficient averages evaporation and transpiration and should be used to

compute ETc for weekly or longer time periods for irrigation water management,

where the averaged effects of soil wetting are acceptable and relevant e.g. in furrow

and sprinkler systems (Allen et al., 2007).

1.2.2.3 Dual crop coefficient

The dual crop coefficient allows for the separation of evaporation and transpiration

such that Equation 1.12 can be written as:

𝐸𝑇𝑐 = (𝐾𝑐𝑏 + 𝐾𝑒) × 𝐸𝑇𝑜 Equation 1.12

Allen et al. (1998) defined the Kcb as the ratio of ETc to ETo when the soil surface

layer is dry, but where the average soil water content of the root zone is adequate to

sustain full plant transpiration. This is best suited for irrigation water management in

micro-irrigation systems where high frequency irrigation is practised and large

variations in day to day soil wetness are experienced.

1.2.2.4 Reference evapotranspiration

Reference evapotranspiration may be expressed based on two reference crops,

clipped, cool-season grass or tall alfalfa, whose common symbols are ETo and ETr,

respectively. One, a 0.12-m tall cool-season clipped grass, follows the definition by

FAO-56 (Allen et al., 1998, 2006) and uses the PM equation with specific

parameterizations that now differ from the original 1998 FAO-56 definition (Figure

1.3) only in the value for bulk surface resistance prescribed for hourly or shorter


26

time-step calculations, where rs was reduced (Allen et al., 2006) from the daily value

of 70 s m−1 to a new value of 50 s m−1 for hourly or shorter periods during daytime.

For ETr the standardized reference surface is the ‘tall’ reference, defined to be very

similar to a 0.5 m tall crop of dense, full-cover alfalfa (lucerne) having surface

resistance of 30 s m−1 for hourly or shorter calculation time-steps during daytime and

45 s m−1 for daily calculation time-steps (Pereira et al., 2015). Crop coefficients (Kc)

may be expressed in relation to clipped, cool-season grass as more often used

(Allen et al., 1998; 2007) or to alfalfa; for which the symbol Kcr is adopted (ASCE-

EWRI, 2005; Allen et al., 2007).

Figure 1. 3. Characteristics of the hypothetical short grass reference crop used for

calculation of ETo in the FAO Penman-Monteith equation (Allen et al.,

1998).

The Penman-Monteith equation standardised for the determination of ETo takes the

following form (Allen et al., 2006; Allen et al., 2007; Pereira et al., 2015):

𝐸𝑇𝑜 =0.408∆(𝑅𝑛−𝐺)+𝛾

𝐶𝑛𝑇𝑎+273

𝑢2𝑉𝑃𝐷

∆+𝛾(1+𝐶𝑑0.34𝑢2) Equation 1.13

where ETo is reference evapotranspiration (mm day-1), Rn is net irradiance at the

crop surface (MJ m-2 day-1), G is soil heat flux density (MJ m-2 day-1), Ta is mean


27

daily air temperature at 2 m height (°C), u2 is wind speed at 2 m height (m s-1), VPD

is saturation vapour pressure deficit (kPa), Δ is slope of the vapour pressure curve

(kPa °C-1), γ is the psychrometric constant (kPa °C-1), Cn is a numerator constant

that changes with reference type and calculation time step and Cd is a denominator

constant that changes with reference type and calculation time-step. The values for

Cn and Cd are presented in Table 1.2. The values for Cn consider the time-step and

aerodynamic roughness of the surface (i.e., reference type). The constant in the

denominator, Cd, considers the time-step, bulk surface resistance, and aerodynamic

roughness of the surface.

Table 1.2. Values for Cn and Cd in equation 1.13 for use when determining

evapotranspiration for short (ETo) and tall (ETr) reference crop (Allen et

al., 2007)

Calculation

time-step

ETo ETr Units for

ETo, ETr

Units for

Rn, G

Cn Cd Cn Cd

Daily 900 0.34 1600 0.38 mm d-1 MJ m-2 d-1

Hourly

(daytime)

37 0.24 66 0.25 mm h-1 MJ m-2 h-1

Hourly

(nighttime)

37 0.96 66 1.7 mm h-1 MJ m-2 h-1

1.2.2.5 Citrus crop coefficients

The standard crop coefficients for citrus published by Allen et al. (1998), which are

largely based on the work of Doorenbos and Pruitt (1977), used for estimating ETc

are presented in Table 1.3. In developing the crop coefficients (Kc and Kcb), the

growing season is divided into four distinct growth stages (i.e. initial, crop

development, mid-season and late season stages) that are related to changes in

water use due to crop development. For a generic citrus crop Allen et al. (1998)

stipulated the lengths of the initial, development, mid-season and late season growth

stages as 60, 90, 120 and 95 days, respectively. However, only the crop coefficients


28

during the initial, mid-season and late season presented in the table are required to

construct the crop coefficient curve.

Table 1.3. Citrus crop coefficient (Kc and Kcb) values for standard climate of RHmin =

45 % and u2 = 2 m s-1 as published for use with FAO Penman-Monteith

ETo (Allen et al. 1998).

Orchard and

ground conditions

Kc ini Kc mid Kc end Kcb ini Kcb mid Kcb end

No ground cover

70 % canopy 0.7 0.65 0.7 0.65 0.6 0.65

50 % canopy 0.65 0.6 0.65 0.6 0.55 0.6

20 % canopy 0.5 0.45 0.55 0.45 0.4 0.5

Active ground cover

70 % canopy 0.75 0.7 0.75 0.75 0.7 0.75

50 % canopy 0.8 0.8 0.8 0.75 0.75 0.75

20 % canopy 0.85 0.85 0.85 0.8 0.8 0.85

NB: subscripts ini, mid and end are incorporated to mean initial, mid-season and end stages of crop growth.

Citrus crop coefficients presented in Table 1.3 either decrease during the mid-

season or are constant throughout the season. This is in contradiction to the general

crop coefficient curve for annual crops where the highest values occur during the

mid-season. The occurrence of the highest crop coefficients during this period in

most crops is probably due to the fact that leaf area of these crops is highest at this

point, which translates into maximum water use at this time. The decrease of citrus

crop coefficient values during the mid-season may be interpreted to mean that as the

atmospheric demand increases, transpiration does not increase at the same rate

(Green and Moreshet, 1984; García Petillo and Castel, 2007; Villalobos et al., 2009).

This behaviour has been linked to strong regulation mechanisms within the citrus

tree hydraulic path (Kriedemann and Barrs, 1981).

The adoption and subsequent use of the FAO-56 crop coefficients in citrus is

regardless of the fact that a wide range of crop coefficients has been reported for the

crop in different growing regions (Table 1.4). Three significant deductions can be


29

made from the data presented in Table 1.4. Firstly, the crop coefficients of Allen et

al. (1998) are all less than one, as opposed to some studies in Table 1.4. Secondly,

the values reported by some of the authors are much lower than those reported by

Allen et al. (1998). Thirdly, some of the crop coefficients referred to in Table 1.4 are

lower in summer (period normally coinciding with the mid-season, which is

associated with active tree growth and fruit production) than in winter which agrees

with the crop coefficients of Allen et al. (1998). According to Goldhamer et al. (2012)

this is generally attributed to the citrus stomata being sensitive to evaporative

demand (the air vapour pressure deficit, VPD), closing under dry, hot, windy

conditions and opening under the opposite conditions. Thus, the Kc in the mild

Mediterranean and coastal climates should be higher than those of more arid, inland

valleys. In addition, in Mediterranean environments, high Kc values in winter reflect

high soil evaporation rates from frequent rainfall during that part of the season.

The factors that affect the water use of citrus trees that were mentioned above will

have an inherent effect on the crop coefficients. These factors include differences in

variety, rootstock, tree spacing, canopy height, ground cover, tillage, leaf area index,

method of estimating reference evapotranspiration, microclimate, irrigation method

and frequency and method of measuring crop evapotranspiration (Snyder and

O’Connell 2007; Naor et al. 2008). Another source of variation that is particular to Kcb

values, that are based on transpiration determined using sap flow methods (i.e.

Rana et al. 2005; Villalobos et al., 2009; Marin and Angelocci, 2011; Villalobos et al.,

2013), is that the Kcb values of Allen et al. (1998) represent the transpiration

component of ETc and a small evaporation component from soil that is visibly dry at

the surface. Although the evaporation component is small, it is not detected by sap

flow methods. To distinguish the two forms, Villalobos et al. (2013) suggested that

sap flow-based crop coefficients should be termed transpiration coefficients (Kt).


30

Table 1.4. Seasonal crop coefficients determined in citrus orchards across the growing regions of the world.

Reference Region ETo Kc

Summera Autumn Winter Spring Summer Autumn Winter Spring

Villalobos et al. (2013) Spain 0.34 0.5 0.27 0.3

Marin and Angelocci (2011) Brazil 4.4 2.7 0.7 0.26

Villalobos et al. (2009) Spain 4.99 5.88 0.44 0.43

Fares et al. (2008) USA 4.40 2.24 0.86 0.69

Snyder and O'Connell (2007) USA 6.27 3.03 1.10 4.13 1.00 1.07 1.15 1.13

Alves et al. (2007) Brazil 4.33 3.49 2.90 4.33 1.05 0.93 0.53 0.69

García Petillo and Castel (2007) Uruguay 4.99 1.77 1.45 4.06 0.64 0.77 0.84 0.83

Romero et al. (2006) Spain 0.7 0.7 0.9 0.7

Rana et al. (2005) Italy 1.04 0.77 0.81 1.16

Yang et al. (2003) Japan 4.40 0.60 0.90 0.60

Castel (1997) Spain 4.69 2.75 1.66 3.68 0.32 0.49 0.36 0.24

Castel et al. (1987) Spain 4.93 2.57 1.53 3.43 0.70 0.77 0.65 0.61

Rogers et al. (1983) USA 4.1 3.13 2.37 4.37 1.04 1.01 0.93 0.81

Hoffman et al. (1982) USA 7.7 4.1 2.27 5.27 0.85 0.83 0.77 0.80

Green and Moreshet (1979) South Africa 6.86 3.15 2.62 4.59 0.80 1.28 0.79 0.62

van Bavel et al. (1967) USA 7.91 3.77 2.25 6.30 0.62 0.72 0.48 0.48

aSeasons were determined according to the equinoxes and solstices, with each season comprising 3 months. Measured data

available for the period in the specific seasons was used for each cited work.


31

Most of the works reported on crop coefficients in citrus in Table 1.4 (i.e. Castel,

1997; Rana et al., 2007; Marin and Angelocci, 2011; Villalobos et al., 2009; Consoli

and Papa, 2013; Villalobos et al., 2013; Marin et al., 2016), and other fruit tree

orchards (Ayars et al., 2003; Girona et al. 2003; Testi et al. 2004; Girona et al., 2005;

Johnson et al., 2005; Paco et al., 2006), have used ETo. This is despite of the fact

that these tall tree crops with a large roughness that can probably be best described

by ETr rather than ETo. The use of the ETo as the principal reference method has

been attributed to its early adoption in FAO24 and the simplicity in cultivating this

reference (clipped, cool season grass) across a wide range of locations and climates

(Pereira et al., 2015). Generally, ETr is about 1.1 to 1.4 times that of ETo due to the

increased roughness and leaf area of alfalfa.

In an attempt to improve on the accuracy of crop coefficients when transferred

amongst different orchards Allen and Pereira (2009) consolidated and formalised the

FAO-56 procedure for estimating the crop coefficients as a function of fraction of

ground cover and crop height.

1.2.3 Estimation of transpiration crop coefficients from fractional ground cover

and crop height

Allen et al. (1998) suggested a procedure for estimating the crop coefficients as a

function of fraction of ground cover and crop height using a plant density coefficient.

The advantage of this method is that it is relatively simple and is based on physical

measurements that can easily be carried out in the field. Allen and Pereira (2009)

further consolidated the concept to enable the estimation of site-specific crop

coefficients based on the fraction of ground covered or shaded by the vegetation, the

height of the vegetation and the degree of stomatal regulation under wet soil

conditions.

Allen and Pereira (2009) conceived the idea of an upper, energy-constrained limit on

Kc that can be adjusted for vegetation without full ground cover, such as orchards.

They defined this upper limit, termed Kc max, as the maximum value for Kc following

rain or irrigation. The value for Kc max is governed by the amount of energy available

for evaporation of water, which is largely encapsulated in ETo. The Kc max varies with


32

general climate, ranging from about 1.05 to 1.30 (Allen et al., 1998; Allen et al.,

2005) as follows:

𝐾𝑐 𝑚𝑎𝑥 = 𝑚𝑎𝑥 ({1.2 + [0.04(𝑢2 − 2) − 0.004(𝑅𝐻𝑚𝑖𝑛 − 45)] (ℎ

3)

0.3

} , {𝐾𝑐𝑏 + 0.05})

Equation 1.14

where RHmin is average daily minimum relative humidity during the growth state or

period and h is the mean plant height (m) during the period of calculation (initial,

development, midseason, or late-season).

Transpiration increases with plant density or leaf area, so does the Kc value (Allen

and Pereira, 2009) until the optimum is reached at a value of maximum canopy

cover, which is usually defined as a leaf area index (LAI) equal to 3. In situations

where full canopy cover is not achieved the Kcb, which correlates with the amount of

vegetation because it represents mostly transpiration, can be expressed in terms of

a density coefficient, Kd, where:

𝐾𝑐𝑏 = 𝐾𝑐 𝑚𝑖𝑛 + 𝐾𝑑(𝐾𝑐𝑏 𝑓𝑢𝑙𝑙 − 𝐾𝑐 𝑚𝑖𝑛) Equation 1.15

where Kcb is the approximation for the basal crop coefficient for conditions

represented by the density coefficient, Kd, Kcb full is the estimated basal Kc during

peak plant growth for conditions having nearly full ground cover (or LAI = 3), and Kc

min is the minimum basal Kc for bare soil (Kcb min is approximately equal to 0.15 under

typical agricultural conditions).

1.2.3.1 Basal crop coefficient during peak plant growth (Kcb full)

Kcb full for large stand size (greater than about 500 m2) can be approximated as a

function of mean plant height and adjusted for climate following Allen et al. (1998)

as:

𝐾cb full = 𝐹r (min(1.0 + 0.1ℎ, 1.20) + [0.04(𝑢2 − 2) − 0.004(𝑅𝐻min − 45)] (ℎ

3)

0.3

)

Equation 1.16

where Fr [0-1] is a relative adjustment factor for stomatal control, h is mean monthly

plant height (m), Parameter Fr applies a downward adjustment (Fr ≤ 1.0) if the

vegetation exhibits more stomatal control on transpiration than is typical of most

annual agricultural crops, a situation that is typical of citrus (Kriedemann and Barrs,

1981). Allen and Pereira (2009) suggested the following calculation for Fr for full


33

cover vegetation, based on the FAO Penman-Monteith equation and assuming full

cover conditions:

𝐹𝑟 ≈∆+𝛾(1+0.34𝑢2)

∆+𝛾(1+0.34𝑢2𝑟𝑙

100) Equation 1.17

where rl is mean leaf resistance for the vegetation in question (s m-1); ∆ is the slope

of the saturation vapour pressure versus air temperature curve (kPa °C-1) and γ is

the psychrometric constant (kPa °C-1). For most annual agricultural crops the value

of rl is 100 s m-1, which sets Fr to 1. Allen and Pereira (2009) suggest a value of 420

s m-1 for the initial and midseason periods and 150 s m-1 at the end of the season for

citrus.

1.2.3.2 Estimation of plant density coefficient (Kd)

According to Allen and Pereira (2009), Kd describes the increase in Kc with increase

in amount of vegetation. The shape of the Kd curve is curvilinear with LAI or fraction

of ground cover because of effects of micro-advection of convective and radiative

energy from exposed soil and height of vegetation. The density coefficient Kd can be

estimated as a function of measured or estimated LAI or as a function of fraction of

ground covered by vegetation.

1.2.3.2.1 Estimation of Kd from LAI

Where LAI can be measured or approximated, Kd can be approximated under

normal conditions using an exponential function by suggested by Allen et al. (1998)

as follows:

𝐾𝑑 = 1 − 𝑒0.7𝐿𝐴𝐼 Equation 1.18

where LAI is defined as the area of leaves per area of ground surface averaged over

a large area with units of m2 m-2. Only one side of green healthy leaves that are

active in vapour transfer is counted.

1.2.3.2.2 Estimation of Kd from ground covered by vegetation

Kd can also be estimated from measurement of ground covered by the vegetation

using the following formula suggested by Allen et al. (1998):

𝐾𝑑 = min (1, 𝑀𝐿𝑓c eff, 𝑓c eff

(1

1+ℎ)) Equation 1.19


34

where ƒc eff is the effective fraction of ground covered or shaded by vegetation [0.01-

1] near solar noon, ML is a multiplier on ƒc eff and is an attempt to simulate hydraulic

resistances within the plant and is expected to range between 1.5-2.0, with a value

of 1.5 recommended for citrus (Allen and Pereira, 2009).

Of the two methods for determining Kd, Equation 1.19 is of practical importance due

to the ease involved in determining fc eff and h. For canopies such as trees fc eff can

be estimated according to Allen et al. (1998) as follows:

𝑓c eff =𝑓𝑐

sin 𝛽≤ 1 Equation 1.20

where β is the mean angle of the sun above the horizon during the period of

maximum ETc and ƒc is the fraction of surface covered by vegetation as observed

from directly overhead. β at solar noon can be calculated as:

𝛽 = arcsin[sin(𝜑) sin(𝛿) + cos(𝜑) cos(𝛿)] Equation 1.21

where φ is latitude and δ is solar declination in radians.

For ready application of the methodology, Allen and Pereira (2009) recommended a

set of generic parameters to be used in conjunction with Equations 1.16, 1.17 and

1.19 for different crops including citrus. Generic parameters for citrus orchards are

presented in Table 1.5. Typical crop coefficients developed from effective ground

cover that have been published for mature citrus orchards are presented in Table

1.6. The rl values in Table 1.5 were estimated by inverting Equation 1.17 after

solving for Fr by inverting Equation 1.16 using known Kcb full values. This procedure

aimed at producing values for Kc and Kcb that agree with literature values, including

those from FAO-56. It is emphasised that values for rl determined by this inversion

are only for reuse in Equation 1.17. Allen and Pereira (2009) advised that rl

computed in this way must be evaluated with caution, and recommend the need to

conduct research to improve the estimation of this parameter.

Nearly all rl values obtained for orchards and vine crops following this approach

exceeded the average value of 100 s m-1 normally associated with annual

agricultural vegetation. This was interpreted by Allen and Pereira (2009) as an

indication of strong degree of stomatal control exhibited by different fruit tree species

under typical growing conditions. In a comparative study Meyer and Green (1981)


35

observed that leaf resistances of citrus trees were much lower than that observed in

soybean and wheat grown under similar environmental conditions. Average leaf

resistances higher than what was suggested by Allen and Pereira (2009) have also

been reported in citrus species e.g. 500 to 2000 s m-1 in Shamouti orange trees

(Cohen and Cohen, 1983), 200 to 8280 s m-1 in Navel orange trees (Dzikiti et al.,

2007) and 295 and 830 s m-1 in oranges (Pérez-Pérez et al., 2008).

Table 1.5. Generic parameters for a citrus crop for estimating crop coefficients.

Orchard ground

conditions

Parameters at initial

and midseason

periods

Parameters at end

of season

ML h (m) fc rl Fr fc rl Fr

No ground

cover

1.5 2 0.25 420 0.71 0.20 150 0.94

Ground cover 1.5 2.5 0.45 420 0.71 0.40 275 0.82

Table 1.6. Citrus values of Kcini, Kc mid, Kc end, Kcbini, Kcb mid and Kcb end for standard

climate of RHmin = 45 % and u2 = 2 m s-1 as expanded from FAO-56

(Allen et al. 1998) for a range of values for effective ground covered by

the tree canopy (fc eff) during the midseason and using the procedure of

Allen and Pereira (2009) with recommended parameter values.

Tree density and

ground conditions

Kcini Kc mid Kc end Kcbini Kcb mid Kcb end

No ground cover

High (fc eff = 0.70) 0.95 0.90 90 0.85 0.85 0.85

Medium (fc eff = 0.50) 0.80 0.75 0.75 0.70 0.70 0.70

Low (fc eff = 0.25) 0.55 0.45 0.45 0.40 0.40 0.40

Active ground cover

High (fc eff = 0.70) 1.00 0.95 0.95 0.90 0.90 0.90

Medium (fc eff = 0.50) 0.95 0.95 0.95 0.85 0.90 0.90

Low (fc eff = 0.25) 0.90 0.90 0.90 0.80 0.85 0.85


36

Citrus trees exhibit high resistances to water movement (van Bavel et al., 1967;

Cohen and Cohen 1983; Syvertsen and Graham 1985; Rodríguez-Gamir et al. 2010)

in the soil-plant-atmosphere continuum that can be detected at leaf level. The

resistance is an essential parameter for understanding the mechanisms of plant

transpiration in citrus orchards. Ideally it would be good to conduct extensive

measurements of leaf resistances using porometry. However, such measurements

are affected by a number of shortcomings which include: (i) sampling of leaf

resistances in the field are not only labour intensive but are further complicated by

the fact that rl varies with leaf age and climatic conditions (van Bavel et al., 1967); (ii)

automation of such measurements cannot be made because the sensor creates an

artificial environment, which may lead to changes in the physiological properties of

the leaf; and (iii) manual measurements performed with hand held porometers do not

allow simultaneous sampling of the leaves exposed to varying levels of solar

radiation by one user (Jarvis, 1976).

When measurements of water use are available, the bulk resistance of a vegetated

surface can be obtained using the top–down approach by inversion of Equation 1.10

(Baldocchi et al., 1991). Transpiration measured using sap flow methods have been

used quite extensively to determine bulk resistances in this manner (Wullschleger et

al., 1998). Researchers have, however, reported these in terms of the bulk

conductance rather than resistances. This is because flux is directly proportional to

the conductance, such that errors in conductance, rather than the resistances are

normally distributed (Campbell and Norman, 2008). The general approach has been

to use such data sets to parameterise models that can predict canopy conductance

as a function of canopy size and environmental variables (e.g. Zhang et al., 1997;

Oguntunde et al., 2007; Villalobos et al., 2009; Granier and Loustau 1994; Green

and McNaughton 1997) for predicting transpiration using Equation 1.10.

1.2.4 Modelling canopy conductance

Stomatal conductance of illuminated leaves has been shown to be dependent upon

current levels and history of the immediate environmental variables, which includes

radiant flux density, ambient carbon dioxide concentration, leaf air vapour pressure

difference and leaf water status (Jarvis, 1976). A number of models have been


37

formulated to describe the behaviour of stomatal conductance in relation to these

environmental variables (Damour et al., 2010). Conductance models can be largely

divided into multiplicative (Jarvis-type) and multiple linear regression models.

1.2.4.1 Jarvis-type model

Jarvis (1976) proposed the first multiplicative model involving radiant flux density

(SR), ambient carbon dioxide concentration (Ca), leaf-air water vapour pressure

difference (VPD), air temperature (Ta) and leaf water status (Ψl), which is of the

following form:

𝑔𝑠 = 𝑔𝑠 𝑚𝑎𝑥ƒ(𝑆𝑅)ƒ(𝐶𝑎)ƒ(𝑉𝑃𝐷)ƒ(𝑇𝑎)ƒ(𝛹𝑙)

Equation 1.22

where gs is the stomatal conductance predicted by the Jarvis model (m s-1), gs max is

the maximum stomatal conductance (m s-1). This complex set of factors modulating

stomatal all at once makes it almost impossible to quantify the effects of each

environmental effect in the field. Controlled laboratory studies have been used to

understand the stomatal responses to each of these factors in citrus and other crops.

Citrus stomata were shown to increase with photosynthetically active radiation until

saturation at around 500 μmol m-2 s-1 (Kriedemann, 1971). Stomata of most plants

response to the increase in atmospheric carbon dioxide concentration by reducing

the stomatal aperture. Although transpiration is reduced photosynthetic assimilation

increases such that water use efficiency is increased. Such responses will have

implications for gas exchange of all terrestrial plants under future elevated

concentrations of carbon dioxide. According to Levy and Kaufmann (1976) citrus

stomata over react to a step-change increase in VPD by opening and closing

rhythmically even when environmental conditions remain constant. Significant

responses of citrus stomata to temperature were observed in the range 20 to 35 oC

with the maximum occurring at 30 oC (Khairi and Hall, 1976). It was also shown that

values of leaf water potential at which appreciable citrus stomatal closure occur (-2

500 to -3 000 kPa) are much lower than typical values averaging -2 300 kPa

observed in irrigated trees (Syvertsen and Lloyd, 1994). As such leaf water potential

does not have a direct impact on stomatal behaviour of well-irrigated citrus orchards.

Based on these facts Syvertsen and Lloyd (1994) concluded that a Jarvis model with


38

functions of SR, Ta and VPD should be sufficient to describe the stomatal

conductance of well-irrigated citrus trees.

By assuming the ‘big-leaf’ theory the Jarvis-type models have been extended to

predict canopy conductance (gc). The model, however, has been parameterised

using the minimum number of weather variables that captures the variations of

canopy conductance, with satisfactory accuracy in several fruit tree species (e.g.

Stewart, 1988; White et al. 1999; MacFarlane et al., 2004; Misson et al., 2004; Noe

and Giersch, 2004; Villalobos et al., 2000; Cohen and Cohen, 1983; Oguntunde et

al., 2007). Results of the application of the Jarvis-type model in citrus orchards are

not consistent. Cohen and Cohen (1983) reported that a Jarvis-type model

containing SR, VPD and Ta poorly (R2 = 0.11) described stomatal resistance of citrus

trees. Oguntunde et al. (2007) on the other hand showed that a similar model could

describe the variations of canopy conductance fairly well (R2 > 0.7). Elimination of

the temperature function did not affect the performance of the model in the case of

Oguntunde et al. (2007).

It is imperative that the aerodynamic conductance (ga) term should be determined in

order for gc to be calculated or predicted using Equation 1.10. However, it has been

argued that in the case of well-ventilated canopies, such as orchards, the effect of ga

on transpiration is far less critical than that imposed by gc (Tan et al., 1978;

McNaughton and Jarvis, 1983). The methods that have been used to determine ga

are reviewed in the next section.

1.2.4.3 Aerodynamic conductance

The transfer of water vapour at the surface of the crop canopy is sustained by

molecular diffusion through a thin skin of air, known as the boundary layer, in contact

with the surface (Monteith and Unsworth, 1990). The resistance to water vapour

movement in this layer is known as boundary layer or aerodynamic resistance and;

is difficult to quantify under field conditions, such that they are usually estimated

using empirical models (Pereira et al., 2006). One model that has been used

frequently for trees with leaves subjected to mutual interference is that proposed by

Landsberg and Powell (1973). The original model is:


39

𝑟𝑎 = 58𝑝0.56 (𝑑

𝑢)

0.5

Equation 1.23

where p is a measure of foliage density to wind, estimated by the ratio between the

tree leaf area and the area of its silhouette projected on to a vertical plane, d is a

characteristic leaf dimension (m), sometimes taken as the square root of the mean

leaf area, and u is the average wind speed (m s-1) at the mid-canopy height.

Rana et al. (2005), working in a Clementine orchard, also developed a model for

estimating boundary layer resistance, which was later used by Oguntunde et al.

(2007) in a citrus orchard. This method relies on indirect estimations of zero plane

displacement height, roughness length governing the transfer of heat and vapour,

roughness length governing momentum transfer, von Karman’s constant and wind

speed measurements. The requirement for wind speed measurements at a certain

height above the canopy is the major drawback to this method. The equation has the

following form:

𝑟𝑎 =𝑙𝑛(

𝑧−𝑑

𝑧𝑜)𝑙𝑛(

𝑧−𝑑

ℎ𝑐−𝑑)

𝑘2𝑢𝑧 Equation 1.24

where k is the von Karman’s constant equal to 0.4, uz is the wind speed (m s-1) at the

z wind measurement height (m), d is the zero plane displacement estimated as d =

0.67hc, zo is the roughness length taken as 0.1hc and hc is the mean orchard height.

Equation 1.23 is usually used by most researchers because of of its simplicity.

1.3 Scope of the study

Long-term studies of citrus ETc are needed to update such information in the South

African industry. This study focussed on the long-term measurement of tree

transpiration in three citrus orchards using the HRM sap flow technique developed

by Burgess et al. (2001). Calibration of the sap flow technique was performed using

the eddy covariance method during the dry season (i.e. winter and autumn) when

evaporation from the orchard floor was considered negligible. Calibration of the HRM

was done by establishing a ‘virtual wound width’ used to convert heat pulse

velocities to transpiration. Crop coefficients have been used quite extensively in

estimating crop water use including citrus orchards. However, the variations among

the recently published crop coefficients have cast doubt on their transferability

among different growing regions. Allen and Pereira (2009) formalised the FAO-56


40

methodology for estimating site-specific crop coefficients using canopy height, a crop

density factor and leaf resistance. Citrus trees exhibit high resistances to water

movement and quantifying their resistance is an important step towards developing

mechanistic models of transpiration in these species. Transpiration measurement at

stem level presents the opportunity to determine canopy conductance, that are

difficult to quantify under field conditions (Blad et al., 1982; Allen et al., 1998), using

a top-down approach. The possibility of using a Jarvis-type canopy conductance

model in conjunction with the Penman-Monteith equation to predict seasonal citrus

transpiration was investigated in three orchards.


41

Chapter 2: Calibration of the heat ratio method (HRM) sap flow technique for

long-term transpiration measurement in citrus orchards

2.1 Introduction

Accurate and reliable methods of measuring water use of fruit tree orchards are

needed to gather information that is necessary to improve available irrigation water

management tools. Amongst the many methods that have been used to measure

tree transpiration, thermometric sap flow techniques have shown considerable

promise (Smith and Allen, 1996; Wullschleger et al., 1998). Some of the advantages

that have led to the popularisation of these methods include that they are easily

interfaced to data loggers for direct automated transpiration measurement; their

applicability is not inhibited by complex terrain and soil heterogeneity within fruit tree

orchards; they allow an estimation of transpiration which has a direct relationship

with productivity; and their relatively high accuracy of measuring orchard water use

as compared to other conventional methods e.g. eddy covariance (Rana et al., 2005)

and soil water balance approaches (Nicolas et al., 2005).

Thermometric techniques that have been employed for sap flow measurements in

woody species can be broadly categorized into heat pulse, heat balance and heat

dissipation methods (Smith and Allen, 1996). Heat pulse velocity (Vh) techniques, the

compensation heat pulse method (CHPM) in particular, have been most widely used,

mainly because they are relatively easy to use and require less power in the field

(Edwards et al., 1997; Conejero et al., 2007). However, CHPM is associated with

limitations, of which the major one is the inability to measure low sap flow rates,

which usually occur at night and under water stress conditions (Becker, 1998).

Burgess et al. (2001) developed the heat ratio method (HRM) as an improvement to

the CHPM in order to cater for low and reverse rates of sap flow in woody species.

The use of this relatively new method of measuring transpiration has not been

independently tested in citrus orchards.

Heat pulse techniques are invasive in nature because the probes are inserted into

the sapwood and require correction for the damage, commonly referred to as

wounding, caused by drilling and constant heating (Swanson, 1994). Conversion of

measured Vh’s to sap volumetric flow is performed using numerical models as a


42

function of a number of wood parameters, which include sapwood water content,

sapwood density and wound width. The most sensitive and difficult parameter to

determine using experimental procedures is the actual wound width (Smith and

Allen, 1996; Fernández et al. 2006; Poblete-Echeverria et al., 2012). Some studies

have used predetermined corrections based on the theoretical calibrations of

Swanson and Whitfield (1981) (e.g., Nicolas et al., 2005, Villalobos et al., 2013) with

visually determined wounding widths (Green and Clothier, 1988; Dragoni et al.,

2005) or empirical calibration factors (Green and Clothier, 1988; Steppe et al., 2010)

to correct for wounding.

It has been demonstrated that for sapwood that is not thermally homogeneous a

“virtual wound width” is usually required to convert heat pulse velocities to volumetric

sap flow with appreciable accuracy (Green and Clothier, 1988; Zreik et al., 2003;

Fernández et al., 2006). Thermal homogeneity has been based on the work of

Swanson (1983) who categorised it on the basis of the sapwood xylem vessels

(particularly the diameter and density). However, there seem to contradicting reports

on the response of wood tissue surrounding the inserted probes during long-term

transpiration measurements. Smith and Allen (1996) suggested that wounding

effects increase with time and the Vh probes should be moved regularly, either to a

different part of the same stem or to a new stem. On the contrary, some studies

seem to suggest that only limited changes occur in xylem properties during long

periods of Vh measurements in some tree species e.g., olives (Fernández et al.,

2001; Giorio and Giorio, 2003; Pernice et al., 2009) and apples (Dragoni et al.,

2005).

Sap flow measurements for determining individual tree transpiration have been

calibrated against independent methods of measuring tree transpiration, which

include weighing lysimeters (Caspari et al., 1993; Nortes et al., 2008), whole tree gas

exchange systems (Dragoni et al., 2005; Pernice et al., 2009), cut tree experiments

(Green and Clothier, 1988; Hatton et al., 1995; Fernández et al., 2001), stem

perfusion experiments (Green and Clothier, 1988; Fernández et al., 2006) and

micrometeorological measurements (Jones et al., 1988; Poblete-Echeverría et al.,

2012). The eddy covariance method has been used in a number of experiments to


43

calibrate sap flow measurements in orchard situations (e.g., Conceição and Ferreira,

2008; Poblete-Echeverría et al., 2012).

Crop evapotranspiration (ETc) measurements using micrometeorological

measurements conducted in orchards, during dry periods with minimal ground cover

when soil evaporation is negligible have shown that water loss from the orchard is

predominantly due to tree transpiration (Rogers et al., 1983; Pernice et al., 2009;

Marin and Angeloci, 2011). ETc measurements conducted during such periods can

be used to calibrate sap flow methods in the field. ETc measurements using

micrometeorological measurements are usually done for short periods of time,

largely because they require constant technical attention by well-trained personnel

and instrumentation is fragile and expensive (Allen et al., 2011). There is therefore a

need to establish the minimum number of ETc measurements required for calibration

of the HRM when it is used for long-term transpiration measurements.

The aim of this work was to calibrate the HRM, for measuring transpiration, against

ETc, measured using the eddy covariance method, in citrus tree orchards during dry

periods when evaporation is assumed negligible. It was hypothesized that citrus

sapwood matrix is not thermally homogeneous such that conversion of measured

heat pulse velocity to transpiration requires an empirical calibration factor which will

be constant for long-term measurements.

2.2 Materials and methods

2.2.1 Experimental Site and Climate

Measurements were conducted in a commercial orchard in the 2008/9 season at

Moosrivier Farm (Schoeman Boerdery Group) about 15 km north of the town of

Groblersdal. The farm is located in the summer rainfall area of Mpumalanga

Province of South Africa (25o 02’ 32.69” S and 29o 22’ 09.76” E) with an altitude of

approximately 900 m.a.s.l. The area receives an average annual rainfall of 535 mm

(Lynch and Schulze, 2006) and has an average minimum air temperature of 12.2°C

and maximum air temperature of 24.6°C (Schulze and Maharaj, 2007). The orchard

was planted in 1997 with ‘Delta’ Valencia orange trees (Citrus sinensis L. Osbeck)

grafted on ‘Swingle’ rootstock, at a spacing of 5.5 m x 2.75 m in a north–south


44

orientation (0° N). Measured leaf area index (LAI) of the orchard was 2.85 m2 m-2.

Every alternate tree was “sandwich” pruned, meaning this tree was pruned narrower

every year to allow for the trees on either side to grow into the pruned space.

“Sandwich” pruned trees are removed once the trees on either side have reached an

adequate size as determined by the grower. Average tree height was 4.1 m. The

orchard was drip irrigated with one line per tree row and pressure compensating

emitters with a discharge of 2 L h-1 spaced 1 m apart. The soil type was sandy loam

with an average of 7-12 % clay in the first 1 m depth. The orchard block was circular

in shape with an average diameter of 595 m which allowed a fetch of 300 m from the

prevailing northerly winds for micrometeorological measurements conducted at the

centre of the circular field (Figure 2.1).

Figure 2.1. Map showing the ‘Valencia’ orange orchard highlighted by the yellow

boarder line. The position of the tower during micrometeorological

measurements is indicated by the Δ on the map.

2.2.2 Sap flow measurements

2.2.2.1 Measurement of heat pulse velocities

Sap flow measurements were conducted at stem level using the heat ratio method

as described by Burgess et al. (2001) on three sample trees in the orchard. Selection

N


45

of the three sample trees that were instrumented was based on a tree stem

circumference survey at the start of the study. Stem circumferences of 40 trees were

measured at a height of 40 cm above the ground and ranged from 32.7 to 47.7 cm.

The results of the survey were then fitted to a normal distribution to establish suitable

circumference ranges to be used and select representative trees to be instrumented.

Table 2.1 shows the ranges of the stem circumference that were established and the

dimensions of the trees that were selected for instrumentation.

Table 2.1. Established circumference size classes (CSC) established, the number

of trees in the class (n), the sample tree representing each class,

sample tree circumference (Sc) and the fraction represented by each

sample tree in the ‘Delta’ Valencia orchard as a percentage (pt).

CSC (mm) n Sc (mm) Probe Depths

(mm)

pt

≤400 12 327 7, 14, 22, 30 17

401-449 34 382 7, 20, 30, 40 49

≥45 24 477 7, 20, 30, 40 34

Four probes were inserted in the sapwood of each tree at various depths from the

bark to capture the radial variation of sap flux density with sapwood depth. The

depths to which the different probes were inserted in each sample tree are shown in

Table 2.1. One measuring probe set consisted of a heater probe and two

thermocouples placed upstream and downstream at a distance of 50 mm (Figure

2.2). The 60-mm long line-heaters were made from 1.8-mm outside-diameter

stainless steel tubing, enclosing a constantan filament. Type T (copper/constantan)

thermocouples were embedded in 2 mm outside diameter polytetrafluoroethene

(PTFE) tubing. Drilling was performed using a drill guide strapped to the tree to

ensure that holes were parallel.

Core samples, with a diameter of 5 mm, were taken using an incremental borer from

trees that closely resembled the chosen trees. Simple measurements showed that

the bark thickness was 5 mm and sapwood depth of the trees was 40 mm. Sapwood

depth was based on wood discolouration. The core samples were preserved in


46

formalin, acetic acid and alcohol and taken to the laboratory for anatomical studies of

the xylem structure.

Figure 2.2. Sap flow probes installed in two trees in the ‘Delta’ Valencia orchard.

Insert shows situation of the probes around a stem of one of the sample

trees.

The Vh for each probe set was calculated following Marshall (1958) as:

𝑉ℎ =𝑘

𝑥𝑙𝑛 (

𝑣1

𝑣2) × 3600 Equation 2. 1

where k is the thermal diffusivity of green (fresh) wood (assigned a nominal value of

2.5 x 10-3 cm2 s-1), x is distance in cm between the heater and either thermocouples

(= 0.5 cm), v1 and v2 are changes in temperature after the heat pulse is released

(from initial temperatures) as measured by the upstream and downstream


47

thermocouples and 3600 converts seconds to hours. Heat pulse velocities were

measured and logged on an hourly basis using a CR10X data logger and an

AM16/32B multiplexer (Campbell Scientific Inc., Logan, Utah, USA).

2.2.2.2 Wounding correction

The heat pulse velocities were corrected for wounding (i.e. xylem tissue mechanical

damage) caused by installation of probes and heating using coefficients b, c, and d

obtained from a numerical model developed by Burgess et al. (2001) using the

following equation:

𝑉𝑐 = 𝑏𝑉ℎ + 𝑐𝑉ℎ2 + 𝑑𝑉ℎ

3 Equation 2.2

where Vc is the corrected heat pulse velocity. The functions describing the correction

coefficients in relation to wound width (w) are as follows:

𝑏 = 6.6155𝑤2 + 3.332𝑤 + 0.9236 Equation 2.3

𝑐 = −0.149𝑤2 + 0.0381𝑤 − 0.0036 Equation 2.4

𝑑 = 0.0335𝑤2 − 0.0095𝑤 + 0.0008 Equation 2.5

The wound width was initially assumed to be equal to the size of the largest drill bit

which was 0.2 cm for the thermocouples (Green and Clothier, 1988; Dragoni et al.,

2005). Visual inspection during the measurement period on a piece of wood

chiselled from one of the trees (Figure 2.3) and after Tree 1 was cut down at the end

of the measurement season (Figure 2.4) revealed a wounding width of 0.2 cm.

2.2.2.3 Determining sap velocity

Sap velocity (Vs) was calculated from the corrected heat pulse velocity using the

equation suggested by Marshall (1958) that was later modified by Barrett et al.

(1995):

𝑉𝑠 =𝑉𝑠𝜌𝑏(𝑐𝑤+𝑚𝑐𝑐𝑠)

𝜌𝑠𝑐𝑠 Equation 2.6

where ρb is the basic density of wood, cw and cs are specific heat capacity of the

wood matrix (1200 J kg-1°C-1 at 20 °C (Becker and Edwards, 1999) and sap (water,

4182 J kg-1 °C-1) at 20 °C (Lide, 1992), respectively, mc is water content of the

sapwood and ρs is the density of water (1000 kg m-3).


48

Figure 2.4. Measurement of the wounding width on a wood sample cut

transversely from the trunk of one of the sample trees at the end of the

measuring season in August 2009 (photo courtesy of Mark Gush).

B A

Figure 2.3. Sample of wood taken

from one of the sample trees for the

determination of wounding width,

sapwood water content and

sapwood density: (A) the sample of

wood just before removal (B)

measurement of the wounding

width and (C) the wood sample

used for measurements

C


49

The sapwood moisture content and basic density were determined on freshly

excised wood samples. The sapwood samples were chiselled from the tree and

immediately placed in a plastic bag to preserve moisture content. The green mass of

the sample was measured; the volume (cm³) was determined by water-displacement

in a beaker and then oven-dried at a constant temperature of 70 °C until there was

no significant change in mass. Sapwood moisture content was calculated as:

𝑚𝑐 =𝑀𝑤−𝑀𝑑

𝑀𝑤 Equation 2. 7

where Mw and Md are wet and dry mass (kg) of the sapwood sample.

The basic density ρb was calculated as:

𝜌𝑏 =𝑀𝑑

𝑉𝑤 Equation 2. 8

where Vw is the volume of the wood sample which is equal to the volume of water

displaced in the beaker.

2.2.2.4 Converting sap velocity to sap flux density

Volumetric flow for individual probes was calculated as the product of sap velocity

(Vs) and cross-sectional area of conducting sapwood represented by the specific.

Integration of sap flux measurements by individual probes to obtain whole stem flux

(Q) was performed following the method of weighted average of heat pulse velocity

with depth as presented by Hatton et al. (1990) using Equation 2.9.

𝑄 = 𝜋[𝑟12 ∗ 𝑣1 + (𝑟2

2 − 𝑟12) ∗ 𝑣2 + (𝑟3

2 − 𝑟22) ∗ 𝑣3 + (𝑟4

2 − 𝑟32) ∗ 𝑣4] Equation 2.9

where vk is the heat pulse velocity measured by sensor k placed between radii rk-1

and rk. Integrated sap flux (assumed to be equal to whole tree transpiration) over the

whole sapwood area, calculated on an hourly basis, was normalised to millimetres of

water by dividing by the area allocated to each tree in the orchard (15.125 m2). The

annular cross-section of the sapwood of the tree was divided into four concentric

annuli as shown in Figure 2.5.


50

Figure 2.5. Idealised cross-sectional areas of four annuli rings represented by probe

sets inserted at different depths in the conducting sapwood of a tree

stem shaded in different colours.

2.2.2.5 Xylem anatomical assessments

Xylem anatomical assessments were conducted on excised stem wood samples

prior to probe insertion and at the conclusion of sap flow measurements in wood

tissue surrounding the drilled holes in order to determine the extent of wounding

caused by implantation of probes in the sapwood of the ‘Delta’ Valencia trees and to

assess the thermal homogeneity of the wood. Transverse sections above and below

the drilled holes, radial sections on both sides of the drilled hole and tangential

sections across the drilled hole were made using a sliding microtome. To aid with

contrast during wood tissue observation sections were stained with safranin and fast

green and observed with a Wild Leitz GMBH light microscope (Abbott Laboratories,

Illinois, USA). Safranin normally dyes lignin red and fast green appears a brilliant

Cambium

Sapwood depth

Centre of the stem

Probe 2

Probe 4

Probe 1

Probe 3

r4

r3

r1

r2

r2


51

green in cytoplasm and cellulosic cell walls (Glime and Wagner, 2013). These stains

are considered generally good for staining plant tissues and hence are normally

used for wood. Photomicrographs of the xylem structure and vessel distribution were

taken with a PowerShot A630 digital camera (Canon Inc., USA) mounted on the

microscope. Average xylem vessel lumen diameter and distance between groups of

vessels were measured with an optical scale on the microscope. To get an overall

picture of the sapwood, individual photos of cross sections, taken in radial sequence,

were then ‘stitched’ together using HP Photosmart Essential software (Hewlett-

Packard Development Company, L.P.).

2.2.3 Measurement of orchard evapotranspiration

ETc measurements to calibrate the sap flow method were conducted in the orchard

during two window periods, from 31 July to 3 August 2008 (winter) and from 21 to 25

of May 2009 (autumn). ETc during the two window periods was measured using the

eddy covariance method by the Hydroscience Research Group of the Council for

Scientific and Industrial Research (CSIR) based in Stellenbosch. The measurement

of ETc during winter 2008 was conducted soon after installation of the Vh system and

the measurement in autumn coincided with the end of the orange fruit growing

season in the orchard. Vh measurements were done throughout the season in fruit

growing season in the orchard.

2.2.3.1 The eddy covariance system

Fluxes of latent (λETc) and sensible heat (H) were measured with an extended open

path eddy covariance (OPEC) system, comprising a Campbell CSAT3 three-

dimensional sonic anemometer and in autumn an LI-7500 open path infrared gas

analyser (LiCor Inc., Lincoln, Nebraska, USA) was used, which were mounted on a

lattice mast 6.2 m above the soil surface at the centre of the field. The fetch

requirements of approximately 300 m were met from all directions. The configuration

of instruments is shown in Figure 2.6. Measurements were sampled at a frequency

of 10 Hz and logged on a CR5000 data logger (Campbell Scientific Inc., Logan,

Utah, USA). Air temperature and humidity were measured using a Vaisala HMP45C

temperature and humidity probe (Vaisala Oyj, Vantaa, Finland). Net irradiance (Rn)

was measured using two net radiometers at 6.4 m above the soil surface (Model


52

240-110 NR-Lite, Kipp and Zonen, Delft, The Netherlands), with one placed above

the trees and the other between the tree rows. Soil heat flux (G) was determined

from four soil heat flux plates (model HFT-S, REBS, Seattle, Washington, USA)

placed within the tree rows and in-between the tree rows at a depth of 80 mm. A

system of four Campbell TCAV-L soil temperature averaging probes at depths of 20

and 60 mm were used to calculate the heat stored above the plates. Volumetric soil

water content in the first 60 mm was measured using a Campbell CS616 time

domain reflectometer. These sensors were connected to a CR23X datalogger and

measurements were performed at 10 Hz frequency, with averages obtained every 30

minutes. In order to ensure that the ETc measured were representative of the

orchard a quality analysis of the high frequency data for the EC was done using

EdiRe software (Campbell Scientific Inc., Logan, Utah, USA). The rotations did not

change the fluxes that much for the Groblersdal site.

Energy balance closure during the winter period was assessed using the energy

balance ratio (EBR) on a daily basis and was calculated as follows:

𝐸𝐵𝑅 = 𝐻+𝜆𝐸𝑇𝑐

𝑅𝑛−𝐺 Equation 2.10

where H, λETc, Rn and G are expressed in MJ m-2 day-1. Throughout the May 2009

measurement period, when the IRGA was used to estimate LE, less than 10 % error

in energy balance measurements was found (i.e. EBR>0.9 or EBR<1.1). In August

2008 the shortened energy balance was used to estimate λETc from measurements

of H, Rn and G.

2.2.4 Calibration of the HRM sap flow technique

Transpiration measured with the sap flow method and up-scaled to orchard level was

compared to ETc measured using the eddy covariance method during the two

window periods i.e. from 1 to 4 August 2008 (winter) and from 21 to 25 of May 2009

(autumn). These periods were chosen because the orchard was expected to have

negligible rates of evaporation of intercepted water from the canopy or ground

surface (due to limited ground cover and the absence of rainfall) as observed in


53

orchards by Rogers et al. (1983), Pernice et al. (2009) and Marin and Angelocci

(2011). The contribution of irrigation water to evaporation was also considered

negligible, since the orchard was drip-irrigated and water was applied directly under

the tree, wetting small areas of soil, which were shaded by the trees. As a result ETc

was expected to equal orchard transpiration.

Figure 2.6. Micro-meteorological instruments including mounted on a lattice mast at

the centre of the ‘Delta’ Valencia orchard (photo courtesy of Mark Gush).

A sensitivity analysis was performed to assess the effect of wound width, sapwood

water content and sapwood density on final transpiration values during the autumn

measurement period. The percentage change in transpiration was determined as a

result of a percentage change in each parameter, which varied between 5 and 30%,

whilst keeping the other parameters at their original values. Based on the results of

the sensitivity analysis and the fact that sapwood water content and density were

estimated using experimental procedures the calibration procedure was targeted on

wound width, as in the case of Zreik et al. (2003) and Fernández et al. (2006).

Net radiometers

Temperature & humidity

sensor

Sonic anemometer

IRGA


54

A wound width termed a “virtual wound width” that could be used in the conversion of

heat pulse velocities to tree transpiration, so that average daily sap flow

measurements of the sample trees matched daily ETc measurements, was

determined using linear regression equations. Using this method, HRM-based

transpiration was initially calculated using different wound widths (2, 3, 4 and 5 mm).

Linear regression equations were then formulated between HRM-based transpiration

and the wound width. A “virtual wound width” that matched HRM-transpiration to ETc

was calculated by inputting the measured ETc into the regression equations. Daily

values were chosen to avoid issues associated with capacitance within the citrus

trees, which could result in time lags between sap flow and ETc measurements.

2.3 Results

2.3.1 Calibration of the HRM sap flow technique

It is evident that when using the observed wound width of 0.2 cm, up-scaled sap flow

underestimated the ETc measured over the orchard using the eddy covariance

method. This underestimation of transpiration during the two measurement periods

ranged from 50 to 192 %. A sensitivity analysis of wound width, sapwood water

content and sapwood density revealed that final transpiration values were in fact

most sensitive to changes in wound width, where a 30 % change in wound width

resulted in an error of 50 % in transpiration (Figure 2.7). Although final transpiration

values were also shown to be fairly sensitive to changes in sapwood density and

sapwood water content, a survey across citrus species revealed these two

parameters to be fairly conservative in well-irrigated citrus trees (Table 2.2). The use

of these conservative values for citrus is therefore likely to result in an error of less

than 13%, which is deemed acceptable.


55

Figure 2.7. Error analysis illustrating resultant percentage error in transpiration from

the HRM due to errors in selected parameters in the up-scaling

equations from Vh’s to transpiration, whilst maintaining all other

parameters at their original value.

Table 2.2. Sapwood water content and sapwood density for various citrus species. A

total of 19 samples were taken, with six from lemon, nine from sweet

orange, two from soft citrus and two from grapefruit.

Parameter Value SD %CV

Sapwood water content (kg kg-1) 0.61 0.8 13.11

Sapwood density (kg m-3) 0.74 0.04 5.41

The slopes, intercepts and R2 values of the regression equations of HRM-

transpiration against wound width on different days are presented in Table 2.3. The

virtual wound widths that were determined by inputting measured ETc into the

regression equations are also shown in Table 2.3. The average virtual wound width

that resulted in good agreement between daily sap flow-based transpiration and daily

ETc measurements during the winter and autumn periods were 3.3 and 3.1 mm,

respectively. Figure 2.8 shows a very good agreement between daily transpiration

-60

-40

-20

0

20

40

60

-60 -50 -40 -30 -20 -10 0 10 20 30 40

Err

or

in t

ran

sp

ira

tio

n (

%)

Error in parameter (%)

Wound width

Sapwood density

Sapwood moisture content


56

(obtained using a virtual wound width of 3.3 mm for the winter period and 3.1 mm for

the autumn period) and ETc.

Table 2.3. Slopes and intercepts of the regression equations used to determine

wounding width by inputting ETc on different days. The R2 values and the

virtual wound widths determined from the regression equations are also

shown.

Date Slope Intercept R2

value

Wound width

(mm)

Winter 2008

31 July 7.25 -0.41 0.99 3.4

1 August 6.79 -0.39 0.99 3.7

2 August 6.62 -0.23 0.99 3.1

3 August 8.08 -0.49 0.99 3.1

Average 3.3

Autumn 2009

21 May 3.83 -0.14 0.99 3.1

22 May 4.17 -0.17 0.99 2.8

23 May 3.62 -0,06 0.99 3.0

24 May 3.81 -0.06 0.99 3.3

25 May 5.67 -0.05 0.99 3.2

Average 3.1

There was a small difference of 2 mm between the average virtual wound widths

obtained in the winter and autumn measurement periods. The average of the two

virtual wound widths, i.e. 3.2 mm, was then used to convert heat pulse velocities to

tree transpiration for the two short-term seasonal crop ETc measurement campaigns.

A comparison of hourly transpiration obtained using the average virtual wound width

with measured ETc resulted in a good agreement between measured ETc and

transpiration from the calibrated HRM for most of the days considered (Figure 2.9).

Regression analysis between transpiration and ETc when forced through the origin

resulted in slopes of 1.21 and 1.07 in winter and autumn.


57

Evapotranspiration (mm day-1

)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Tra

nspiration (

mm

day

-1)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Winter

Autumn

Figure 2.8. Comparison between daily transpiration obtained using a virtual wound

width of 3.3 mm for the winter period and 3.1 mm for the autumn period.

2.3.3 Xylem anatomy

A ‘stitched’ transverse section of the citrus sapwood before the insertion of the

probes illustrates that citrus trees have diffuse–porous xylem anatomy i.e. early- and

latewood pores show little variation in size or density (Figure 2.10A). The xylem

elements occur in two to four radial groups or clusters, which form the xylem vessels.

Measured average lumen diameter of the xylem vessels was (0.15 ± 0.02) mm and

the average distance between clusters was (0.8 ± 0.22) mm. Figure 2.10B is a

photograph of the position of a heater probe in the sap wood of one of the

instrumented trees showing the extent of the damage caused by drilling and constant

heating. The average wound width that was observed for all the probes by the naked

eye was 0.2 cm. Tangential sections around the same hole showed blocked xylem

elements appearing as dark stripes as illustrated in Figure 2.10C. The discolouration

of ray cells and vessels blocked with gum (g) and phenols (p), that extend for at least

6 mm from the drilled holes (Figure 2.10D), which could also be seen a transverse

section of the sapwood approximately 1 mm above the downstream thermocouple


58

(Figure 2.10E), suggests that the effective wounding caused by drilling and heating

extends beyond the visible wound width of 2 mm.

21-May-09 22-May-09 23-May-09 24-May-09 25-May-09 26-May-09

0.00

0.05

0.10

0.15

0.20

0.25

31-Jul-08 01-Aug-08 02-Aug-08 03-Aug-08 04-Aug-08

Evap

otr

anspir

ation

and

Tra

nspir

ation

(m

m h

-1)

0.0

0.1

0.2

0.3

0.4

Transpiration

Evapotranspiration

Date

Winter

Autumn

Figure 2.9. Up-scaled HRM-based transpiration using a “virtual wound width” of 3.2

mm as compared to micrometeorological measurements of

evapotranspiration.


59

Figure 2.10. Photomicrographs of sapwood samples taken from a ‘Valencia’ orange

tree. (A) A transverse section of the citrus sapwood prior to probe

insertion showing the distribution of the xylem vessels (x) in the

sapwood; (B) a transverse section of sapwood adjacent to one of the

drilled holes made for insertion of a probe; (C) tangential section

adjacent to one of the drilled holes showing the affected rays; (D) a

transverse section showing the extent of blockage of xylem vessels by

gum (g) and phenols (p); and (E) a transverse section of the sapwood

approximately 1 mm above the downstream thermocouple showing

extensive xylem blockage. Scale bars on each photograph are equal to

2 mm.

A

C

D

E

Hole

Blocked xylem vessel

vessels

x

g p

Hole

B


60

2.4 Discussion

Heat pulse velocity techniques have been used extensively to estimate transpiration

of fruit trees (Nicolas et al., 2005; Rana et al., 2005; Pernice et al., 2009; Marin and

Angelocci, 2011; Consoli and Papa, 2013). There is serious concern that this

technique tends to underestimate transpiration (Green and Clothier 1988; Jones et

al., 1988; Steppe et al., 2010), and species-specific calibration is therefore required

(e.g., Green and Clothier, 1988; Green et al., 2003; Dragoni et al., 2005; Ferandez et

al. 2006; Pernice et al., 2009). This is because of the invasive nature of the methods

that disrupts the sap stream and alters the thermal homogeneity of the sapwood

surrounding the probes causing a systematic underestimation in the measured Vh’s

(Cohen et al., 1981; Green and Clothier, 1988). In this study sap flow measurements

using the HRM were calibrated using eddy covariance measurements of ETc under

field conditions in an orchard planted with ‘Delta’ Valencia orange trees, when

evaporation was considered to be negligible.

The small difference between the virtual wound widths determined during the two

measurement periods used for calibration, which were nine months apart, indicates

that limited changes occurred in the sapwood surrounding the probes during the

measurements. As the initial calibration was performed immediately after the

insertion of the probes it can be inferred that wounding in response to probe insertion

in citrus occurs quickly and once established it does not change over time. As such a

single calibration using this method is most probably sufficient for long-term

measurement of transpiration using the HRM in citrus. In addition, the use of a virtual

wound width of 3.2 mm resulted in very good agreement between transpiration

determined by the HRM and ETc suggesting that this is a reliable method for in-field

calibration of sap flow systems. Constant wound widths or correction factors for long

term sap flow measurements have also previously been reported. Dragoni et al.

(2005) reported a constant wounding effect over a period of two and half months in

apples. Rana et al. (2005) also used a constant correction factor over a period of one

month in citrus trees. This is, however, in contradiction to earlier findings where

changes in wound width were observed to occur with time (Swanson and Whitfield,

1981; Marshall et al., 1981; Zreik et al., 2003).


61

Although there are no reports of the calibration of the HRM in citrus in literature to

draw comparisons with, similar calibrations of other Vh techniques do exist. The

average virtual wound width of 3.2 mm that could be used to match orchard

transpiration to ETc for both measurement periods is similar to the range of values

(2.8-3.2 mm) determined by Zreik et al. (2003) in citrus. However, it is greater than

the virtual wound width of 2.4 mm determined in citrus by Fernández et al. (2006).

Differences would be expected due to the fact that experimental conditions and

analytical equations used by the authors are not the same as those used in this

study. This includes the fact that they were using a different sap flow method (i.e. the

compensation heat pulse technique) with different wound correction analytical

models. In addition both experiments were not carried out under field conditions but

were cut tree experiment (Fernández et al., 2006) and transpiration based on mass

changes of potted plants (Zreik et al., 2003).

There are two possible explanations that could be drawn from the xylem anatomical

assessments that could have led to a virtual wound width that is greater than what

was observed with the naked eye. Firstly, the diameter of the xylem vessels and the

distance between them is greater than 0.4 mm, which may cause the sapwood

matrix of the citrus trees to depart from the assumption of thermal homogeneity and

therefore may not adhere to the underlying principles of the Vh techniques as

theorised by Huber and Schmidt (1937). Studies by Swanson (1983), Green and

Clothier (1988) and Fernández et al. (2006) concluded that distances of non-

conductive tissue greater than 0.4 mm tend to cause departures from thermal

homogeneity such that an effective wound width greater than the largest hole drilled

would be required to convert Vh’s to transpiration. This is not taken into account in

the wound correction process, based on the numerical models of Burgess et al.

(2001) used in this study. Secondly, the greater virtual wound width is also probably

due to the fact that besides the interruption of flow pathways (caused by mechanical

damage during sensor installation) intact vessels had become occluded as the plant

responded to wounding by deposition of gum and phenols. According to Burgess et

al. (2001) such occlusions, which may not be visible to the naked eye, result in a

region of non-conducting wood around the site of probe insertion, which has an

effect of decreasing the heat ratio (v1/v2) and hence Vh in Equation 2.3.


62

2.5 Conclusions

The HRM was successfully calibrated under field conditions in a citrus orchard using

ETc estimated from the eddy covariance method. It was established that a virtual

wound width of 3.2 mm can be used in the conversion of heat pulse velocities to tree

transpiration for both measurement periods (winter 2008 and autumn 2009) so that

average daily sap flow measurements of the sample trees matched daily ETc

measurements done using the eddy covariance method. The virtual wound width

that was greater than the biggest hole drilled (2 mm) was probably due to the fact

that citrus wood is not thermally homogeneous as indicated by the xylem anatomical

assessments. This in-field calibration method was performed twice, with nine months

of continuous heat pulse velocity measurements separating the measurement

windows, indicating the likelihood that the wound width remained constant

throughout this period. The use of a single virtual wound width during the two

measurement periods resulted in a good match between transpiration and ETc

thereby suggesting that the HRM is reliable for long-term measurements of

transpiration in citrus; and a single calibration using this method may be sufficient for

long-term transpiration measurements. The development of a constant “virtual”

wound width for citrus is a novel approach which will in future allow the online

calculation of the sap flux density for potential real time monitoring of citrus tree

transpiration.


63

Chapter 3: Measurement of long-term transpiration and transpiration

coefficients in citrus orchards

3.1 Introduction

Irrigation plays a major role in meeting crop water requirements for evergreen citrus

orchards, which require water all year round in semi-arid regions, such as South

Africa (Bijzet, 2006). Micro-irrigation systems, such as drip, that allow for greater

control over the quantity of water applied, have been adopted by citrus farmers in

South Africa in recent years. The potential of drip irrigation systems to improve

irrigation water use efficiency in orchards lies in their ability to supply near-to-exact

the water required by the tree crops; and the fact that it applies water directly to the

root system on small areas which are usually shaded, thereby limiting evaporation

(Reinders et al., 2010)

However, there is a need to complement these systems with water management

procedures that are system-specific, if their benefits are to be fully realized.

Knowledge of the water use of crops and the factors that govern the actual process

of water uptake are essential for developing models that are used for extrapolating

such information for irrigation water management. Such knowledge is considered

lacking under the relatively new micro-irrigation systems in South Africa (Pavel et al.,

2003; Volschenk et al., 2003). The need to update such information is also

necessitated by a change in rootstock choice from the more vigorous ‘Rough Lemon’

to the rootstocks of intermediate vigour which include ‘Carrizo’, ‘Troyer’ and

‘Swingle’. Thermometric sap flow techniques can be utilised to expedite the

gathering of information on transpiration of citrus orchards to fill that knowledge gap.

The heat ratio method (HRM) sap flow technique has been used to study

transpiration dynamics in Jatropha curcas L. (Gush, 2008), olive (Williams et al.,

2004; Er-Raki et al., 2010), Eucalyptus marginata (Bleby et al., 2004) and Prosopis

(Dzikiti et al., 2013).

The crop coefficient (Kc) approach proposed by Doorenbos and Pruitt (1977) that

was later refined by Allen et al. (1998) has been used quite extensively in irrigation

water management of various crops including citrus (e.g., Green and Moreshet,

1979; Hoffman et al., 1982; Rogers et al., 1983; Castel et al., 1987; Castel, 1997;


64

Allen et al., 1998; Yang et al., 2003; Rana et al., 2005; Fares et al., 2008). This has

been attributed to the relative simplicity of the method such that it is currently

considered the standard method for determining crop water use (Pereira et al.,

2015). One major advantage of the crop coefficient approach is that it considers the

independent contributions of soil evaporation and crop transpiration towards crop

evapotranspiration (ETc) (Allen et al., 1998). This is done by using the dual crop

coefficient approach in which Kc is split into two separate coefficients, i.e. a soil

evaporation coefficient (Ke) and the crop transpiration coefficient (Kcb).

Recent studies have, however, revealed variability in crop coefficients of citrus

among different growing regions (Carr, 2012; García Petillo and Castel, 2007) and

the need to up-date crop coefficients has been highlighted (Snyder and O’Connell,

2006). One source of variation that is particular to Kcb values that are based on

transpiration determined using sap flow methods (e.g., Rana et al. 2005; Villalobos

et al., 2009; Marin and Angelocci, 2011; Villalobos et al., 2013) is that the Kcb values

of Allen et al. (1998) represent the transpiration component of ETc and a small

evaporation component from soil that is visibly dry at the surface. Although the

evaporation component is small, it is not determined by the sap flow methods. To

distinguish the two forms, Villalobos et al. (2013) suggested that sap flow-based crop

coefficients should be termed transpiration coefficients (Kt).

The aims of this work were to: (i) quantify the long-term transpiration of three well-

irrigated citrus orchards using the HRM, (ii) determine Kt values of citrus orchards

based on transpiration measured using the HRM, and (ii) verify the suitability of the

Kcb values proposed for a generic citrus crop in the FAO56 to predict transpiration of

citrus orchards.


3.2.1 Experimental site and climate

Measurement of tree water use was conducted at Moosrivier Farm (Schoeman

Boerdery Group) in commercial orchards planted with ‘Delta’ Valencia and

‘Bahianinha’ Navel oranges [Citrus sinensis (L.) Osbeck]. The description of the


65

‘Delta’ Valencia orange tree orchard and equipment setup is given in Section 2.2.1.

Measurements were conducted during the 2008/9 season in the ‘Delta’ Valencia

orchard and during the 2009/10 in the ‘Bahianinha’ Navel orchard. The ‘Bahianinha’

Navel orange trees were grafted on ‘Carrizo’ rootstocks and were planted in 2003.

The row orientation was 51o ENE, with north being 0o. Tree spacing was 6 m x 2 m

with the trees planted on ridges, pruned to an average height of 2.5 m each year

after harvest. Measured leaf area index (LAI) of the orchard was 2.34 m2 m-2. The

orchard was drip-irrigated, with one line per tree row and pressure compensating

emitters with a discharge of 2.3 L h-1, spaced 1 m apart. The soil type was sandy

loam with an average of 5-10 % clay in the first 1 m depth.

Both orchards were managed according to commercial standards, as stipulated by

the GLOBALG.A.P standards. Irrigation scheduling was done using a simple water

balance approach checked with soil water content measurements performed using

DFM capacitance probes (DFM Software Solutions, South Africa). Generally, both

orchards received irrigation on a daily basis, with two to three 2-h pulses per day,

which ensured that soil water content was maintained near to field capacity.

An additional data set of transpiration and ETo measurements that was sourced from

within the “Water use of fruit tree orchards” project, of which this study was part of,

will also be reported on. The measurements were conducted in a commercial

orchard planted with ‘Rustenburg’ Navels in the 2010/11 season at Patrysberg Farm

in the Western Cape Province (32° 27’ 15.43’’ S and 18° 58’ 3.58’’ E, 149 m.a.s.l.)

near Citrusdal, in the winter rainfall region of South Africa. The area receives an

average annual rainfall of 200 mm and has average minimum and maximum

temperatures of 10 °C and 24 °C, respectively. The ‘Rustenburg’ Navel trees were

grafted on ‘Troyer’ citrange rootstocks and were planted in 1996. Tree spacing was 5

× 2.5 m with trees being pruned shortly after harvest to a height of 3.2 m, with

selective limb removal, according to the industry standards of the production area.

The orchard row orientation was 79° ENE. Average tree height was 3.3 m. Measured

leaf area index (LAI) of the orchard was 3.40 m2 m-2. The orchard was drip-irrigated,

with two drip lines per tree row using pressure compensating emitters spaced 0.8 m

apart with a discharge of 1.8 L h−1. The soil texture was a sandy loam with an


66

average of 5–10 % clay in the top 1-m depth. The orchard was irrigated on a daily

basis, with one 2 to 3 h pulse per day.

3.2.2 Estimation of transpiration

Heat pulse velocities (Vh) were measured using the HRM developed by Burgess et

al. (2001) on three sample trees in the ‘Delta’ Valencia orchard, four sample trees in

the ‘Bahianinha’ Navel orchard and six trees in the ‘Rustenburg’ Navel. Details of the

instrumentation in the ‘Delta’ Valencia orchard were given in Section 2.2.2. Selection

of the sample trees that were instrumented in the other orchards was also based on

a tree stem circumference survey as described the ‘Delta’ Valencia orchard in

Section 2.2.2. Table 3.1 shows circumference size classes established, the number

of trees in each class, the sample tree representing each class, sample tree

circumference and the percentage of the orchard represented by each sample tree in

the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards. No heartwood was detected on

core samples taken from other trees in three orchards using an incremental borer.

The details of the measurement procedure of the Vh’s and conversion to

transpiration volumes are given in Section 2.2.2. The integrated sap flux density

(assumed to be equal to transpiration) was calculated for every hour and then

summed to obtain daily transpiration. The virtual wound width that was established

for the ‘Delta’ Valencia orchard using micrometeorological measurements in Chapter

2 was used in the three orchards.


67

Table 3.1. Established circumference size classes (CSC), the number of trees in the

class (N), the sample tree representing each class, sample tree

circumference (Sc) and the percentage represented by each sample tree

each orchard (Pt).

CSC (mm) N Sc (mm) Probe depths

(mm)

Pt

‘Bahianinha’ Navels

≤282.7 24 222 7, 14, 22, 30 16.00

282.8-306.3 26 306 7, 20, 30, 40 18.00

306.4-342.4 55 313 7, 20, 30, 45 37.00

≥342.5 42 346 7, 20, 30, 40 29.00

‘Rustenburg’ Navels

≤300 6 280 8, 15, 25, 30 21.10

300-350 15 345 8, 15, 25, 30 32.40

350-390 15 384 10, 18, 30, 40 8.45

350-390 11 392 10, 18, 30, 40 8.45

390-430 12 442 10, 18, 30, 40 21.10

>430 12 444 10, 18, 30, 40 8.50

Integrated volumetric sap flow of the individual trees (L day−1) was converted to

transpiration (mm day−1) using the ground area allocated to each tree in the orchard,

i.e. 12 m2 in the ‘Bahianinha’ Navel orchard and 12.5 m2 in the ‘Rustenburg’ Navel

orchard. Orchard transpiration in the two orchards was calculated as a weighted

average of sampled trees as suggested by Hultine et al. (2010), based on a stem

circumference survey at the start of the study and the consistent relationship

between seasonal water use and stem circumference (Figure 3.1). Transpiration of

the ‘Delta’ Valencia orchard was calculated as an average of the sample trees as a

result of the sandwich pruning method adopted in this orchard, which resulted in a

significantly smaller canopy in every second tree. In the ‘Bahianinha’ and

‘Rustenburg’ Navel orchards where trees were pruned to almost an equal canopy

size, it was thought that the stem diameter would have an influence on the

transpiration rate.


68

Trunk circumference (cm)

0 10 20 30 40 50

Tota

l w

ate

r use (

mm

)

0

200

400

600

800

1000

'Rustenburg' Navels

'Bahianinha' Navels

y = 2.744x1.4507

R2 = 0.9963

y = 2.8608x1.4589

R2 = 0.9978

Figure 3.1. Relationship between trunk circumference and seasonal water use for

the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards

3.2.3 Reference evapotranspiration

Weather variables required for the determination of reference evapotranspiration

(ETo) were recorded using an automatic weather stations (AWS) installed at both

sites. The weather variables that were recorded included wind speed, solar radiation,

temperature, relative humidity and rainfall. The AWS at Groblersdal was located on

an open stretch of mown, rain-fed grass and was 50 m west of natural vegetation,

which consisted of sparse trees (2-3 m tall) and grasslands. There were buildings to

the east, within 130 m of the AWS, and irrigated orchards within 300 m to the north.

Under these fairly dry conditions, reference evapotranspiration (ETo) is likely to be

slightly overestimated, as compared to the reference surface (Allen, 2008). This is as

a result of high VPD that occurs over the equilibrium boundary layer over a dry

surface as compared to a well water grass surface theorised by Allen et al. (1998).

The AWS at Citrusdal was located on the site of a recently top-worked (1 m height),

ridged and drip irrigated orchard, with a short ground cover consisting of grass and

weeds. It was 20 m east of an irrigated orchard with a height of 3 m, which would


69

have reduced wind speed and therefore ETo is likely to be somewhat

underestimated, as compared to standard conditions (Allen 2008).

Quality assessment and quality control of the data was performed according to the

procedures described by Allen (2008). The “upper” measured values of solar

radiation (Rs) fell routinely below the clear-sky short wave radiation (Rso) curve and

Rs measurements were therefore adjusted upwards based on the average value of

Rs/Rso on clear days (Allen 2008).

Daily ETo was determined using the FAO-56 Penman-Monteith equation following

Allen et al. (1998):

𝐸𝑇𝑜 =0.408∆(𝑅𝑛−𝐺)+𝛾

900

𝑇𝑎+273𝑢2(𝑉𝑃𝐷)

∆+𝛾(1+0.34𝑢2) Equation 3.1

where ETo is reference evapotranspiration (mm day-1), Rn is net radiation at the crop

surface (MJ m-2 day-1), G is soil heat flux density (MJ m-2 day-1), Ta is mean daily air

temperature at 2 m height (°C), u2 is wind speed at 2 m height (m s-1), VPD is water

vapour pressure deficit (kPa), Δ is slope of the vapour pressure curve (kPa °C-1) and

γ is the psychrometric constant (kPa °C-1).

3.2.4 Determination of transpiration (Kt) crop coefficients

According to Villalobos et al. (2013) the basal coefficient of Allen et al. (1998)

includes some soil evaporation which makes it difficult to separate the two

components of ETc effectively. An equivalent of the basal crop coefficient, termed the

transpiration coefficient (Kt) as suggested by Villalobos et al. (2013), was determined

from measured tree transpiration and ETo as follows:

𝐾𝑡 =𝑇

𝐸𝑇𝑜 Equation 3.2

where Kt is the basal crop coefficient and T is transpiration estimated from sap flow

measurements. Monthly crop coefficients were calculated from monthly totals of

measured daily orchard transpiration and ETo. Monthly crop coefficients were

calculated as citrus is an evergreen crop and significant changes in canopy size do

not occur on a weekly basis.


70

3.3 Results and discussion

3.3.1 Measurement of long-term transpiration

Measured transpiration rates in the three orchards showed large day to day

variations, which were largely determined by changes in atmospheric evaporative

demand, defined in terms of ETo (Figure 3.2). At Groblersdal the recorded ETo in the

2008/9 season ranged from 0.93 mm day-1 to 8.04 mm day-1. Transpiration in the

‘Delta’ Valencia orchard on the days when minimum and maximum ETo were

measured were 0.24 and 1.92 mm day-1 respectively. ETo in the 2009/10 season

ranged from 0.71 mm day-1 to 7.93 mm day-1. Transpiration of ‘Bahianinha’ Navel

orange trees on the days with minimum and maximum ETo were 0.08 and 1.63 mm

day-1, respectively. ETo in the 2010/11 season at Citrusdal ranged from 0.59 to 9.58

mm day-1 and; transpiration rates measured in the ‘Rustenburg’ Navel orchard on

those respective days were 0.26 and 2.16 mm day-1. Maximum transpiration rates

recorded in all the orchards were not on days with the maximum ETo.

Differences in transpiration measured in the orchards become more evident when

the average rates for the different seasons (i.e. summer and winter) are considered

(Table 3.2). Similar seasonal averages have also been calculated by other scientists

(Moreshet and Green, 1983; García Petillo and Castel, 2007) for easy comparison

with other data. Transpiration rates were generally higher in the ‘Delta’ Valencia

orchard than in the ‘Bahianinha’ Navel orchard despite the close similarities in the

atmospheric evaporative demand. This was largely attributable to the fact that the

‘Delta’ Valencia trees were bigger in size as compared to the ‘Bahianinha’ Navel

trees. Furthermore, although higher atmospheric evaporative demands were

observed in Citrusdal during the summer months (winter rainfall region), the

‘Rustenburg’ Navels did not use proportionally more water as compared to the ‘Delta’

Valencia orchard in Groblersdal (summer rainfall region), even though canopy size

was similar. This has previously been noted by Kaufmann (1977), who observed that

although evaporative demand was much higher under Arizona desert conditions, as

compared to the humid conditions in Florida, citrus transpiration was very similar in

summer in these two regions.


71

30-J

ul-08

19-A

ug-0

8

08-S

ep-0

8

28-S

ep-0

8

18-O

ct-

08

07-N

ov-0

8

27-N

ov-0

8

17-D

ec-0

8

06-J

an-0

9

26-J

an-0

9

15-F

eb-0

9

07-M

ar-

09

27-M

ar-

09

16-A

pr-

09

06-M

ay-0

9

26-M

ay-0

9

15-J

un-0

9

05-J

ul-09

25-J

ul-09

Re

fere

nce

Eva

po

tra

nsp

ira

tio

n a

nd

Tra

nsp

ira

tio

n

(mm

da

y-1

)

0

2

4

6

8

10

Reference Evapotranspiration

Transpiration

01-S

ep-0

9

21-S

ep-0

9

11-O

ct-

09

31-O

ct-

09

20-N

ov-0

9

10-D

ec-0

9

30-D

ec-0

9

19-J

an-1

0

08-F

eb-1

0

28-F

eb-1

0

20-M

ar-

10

09-A

pr-

10

29-A

pr-

10

19-M

ay-1

0

08-J

un-1

0

28-J

un-1

0

18-J

ul-10

0

2

4

6

8

10

'Bahianinha' Navels

'Delta' Valencia

Date

13-A

ug-1

0

02-S

ep-1

0

22-S

ep-1

0

12-O

ct-

10

01-N

ov-1

0

21-N

ov-1

0

11-D

ec-1

0

31-D

ec-1

0

20-J

an-1

1

09-F

eb-1

1

01-M

ar-

11

21-M

ar-

11

10-A

pr-

11

30-A

pr-

11

20-M

ay-1

1

09-J

un-1

1

29-J

un-1

1

19-J

ul-11

08-A

ug-1

1

0

2

4

6

8

10

12

'Rustenburg' Navels

Figure 3.2. Daily transpiration and reference evapotranspiration determined in the

‘Delta’ Valencia, ‘Bahianinha’ and ‘Rustenburg’ Navel orchards.


72

Table 3.2. Average daily transpiration (T) and reference evapotranspiration (ETo) for

the summer and winter seasons in the three orchards.

Orchard T (mm day-1) ETo (mm day-1)

Summer Winter Summer Winter

‘Delta’ Valencia 2.30 1.16 5.75 2.57

‘Bahianinha’

Navel 1.90 0.65 6.09 2.53

‘Rustenburg’

Navels 2.26 2.08 6.42 1.62

Published work on seasonal water use of citrus orchards under South African

conditions is available in the form of classic work done over two decades ago – a

knowledge gap that prompted this study. Transpiration of a basin-irrigated 15-year

old Valencia orchard measured by Green and Moreshet (1979) in weighing

lysimeters ranged from 1.9 to 5.8 mm day-1, with an average of 2 mm day-1 in winter

and 4.97 mm day-1 in summer. The reference evapotranspiration measured using a

class ‘A’ pan during the same period ranged between 2.5 and 7.6 mm day-1, which is

very similar to the environment in which this study was conducted. The seasonal

transpiration figures were higher than the values in the current study partly because

the trees were older and transpiration (mm) was calculated from the wetted area,

instead of the area allocated to the tree. If these values are normalised using the

area allocated to each tree, transpiration would range from 0.69 to 1.73 mm day-1

which is comparable to what was established in this study.

Daily transpiration measured in the three citrus orchards was within the range of ETc

(0.7 to 8.5 mm day-1) reported in citrus tree species across the different growing

regions of the world (García Petillo and Castel, 2007; Carr, 2012). However, there

are few studies in which long-term transpiration of citrus orchards was measured

using sap flow techniques in other regions that can be compared with this study.

Transpiration rates measured in this study were lower than 4 mm day-1 in summer

and 1 mm day-1 in winter reported by Rana et al. (2005) under Mediterranean


73

conditions. The difference can most likely be ascribed to the manner in which

transpiration volumes (L) are converted to mm, as described above. Rana et al.

(2005) used the base of the tree crown to convert L to mm day-1, whilst in this study

the area allocated to each tree was used. Consoli and Papa (2013) also measured

transpiration rates greater (0.5 to 6 mm day-1) in semi-arid Mediterranean conditions

than what was observed in this study likely because the trees were older and had a

larger canopy (LAI ranging from 4.0 to 4.7) than those in this study.

Besides canopy size, an additional factor which may have contributed to the lower

transpiration in the ‘Delta’ Valencia and ‘Bahianinha’ orchards used in this study than

other orchards (including the ‘Rustenburg’ Navel orchard reported here), is the lower

than average yields attained during the monitoring periods. The yields for the ‘Delta’

Valencia and ‘Bahianinha’ orchards of 28 and 15 t ha-1, respectively, were

considerably lower than the average yields for these orchards and much lower than

the 75 t ha-1 recorded in ‘Rustenburg’ Navel orchard. There are reports of crop load

impacting gaseous exchange (Syvertsen et al., 2003), as well as sap flow rates

(Yonemoto et al., 2004), with lower crop yields having a negative feedback on

photosynthesis and stomatal conductance, through carbohydrate accumulation in

leaves. Differences in transpiration between Valencia and Navel trees may be due to

different varietal, as well as the rootstock-scion combinations as reported previously

(Yonemoto et al., 2004; Rodríguez-Gamir et al., 2010). However, despite all of these

factors transpiration rates measured in this study are comparable to 0.4 to 2.3 mm

day-1 that was reported by Marin and Angelocci (2011) in Southern Brazil, and 0.1 to

2.5 mm day-1 reported by Villalobos et al. (2013) in East and South Spain. It is

therefore evident that citrus transpiration, on both a daily and seasonal basis, varies

quite dramatically across the different growing regions of the world.

Transpiration was measured for periods of 364 days in the ‘Delta’ Valencia, 301 days

in the ‘Bahianinha’ Navels and 365 days in the ‘Rustenburg’ Navels. Total

transpiration for the measurement periods were 682 mm, 468 mm and 672 mm in

the ‘Delta’ Valencia, ‘Bahianinha’ and ‘Rustenburg’ Navel orchards, respectively

(Table 3.3). The total rainfall and irrigation volumes recorded for each orchard also

shown in Table 3.3 exceeded transpiration suggesting that the trees were not water

stressed. Irrigation management was assumed to be very good especially given the


74

fact that these were the best growers producing export quality citrus. Rana et al.

(2005) measured a seasonal transpiration totalling 766 mm using sap flow, which is

higher than what was recorded in the ‘Delta’ Valencia orchard of similar age.

Although cumulative transpiration could not be ascertained in the cases of either

Marin and Angelocci (2011) or Villalobos et al. (2013) the close similarity of the daily

magnitudes would most likely translate to the same effect on a seasonal basis. Total

crop evapotranspiration, including evaporation in citrus orchards, has been

estimated to be in the range of 767 mm yr-1 in Uruguay (García Petillo and Castel,

2007) to over 1400 mm yr-1 in Florida USA (Fares et al., 2008).

Table 3.3. Accumulated reference evapotranspiration (ETo), rainfall, irrigation and

transpiration for the measurement periods in each orchard.

Accumulated

water (mm) ‘Delta’ Valencia

‘Bahianinha’

Navel

‘Rustenburg’

Navels

ETo 1668 1423 1528

Rainfall 579 518 203

Irrigation 925 261 600

Transpiration 682 468 672

3.3.2 Determination of transpiration crop coefficients (Kt)

There was a lot of variation in the day-to-day Kt coefficients determined in the three

orchards (Figure 3.3). The ranges for the Kt values determined were 0.14-0.78 in the

‘Delta’ Valencia orchard, 0.12-0.59 in the ‘Bahianinha’ Navel orchard and 0.22-1.21

in the ‘Rustenburg’ Navel orchard. Differences in the Kt values can be observed

when average monthly Kt (Figure 3.4) and seasonal Kt (Table 3.4) values were

determined. The monthly Kt coefficients were fairly constant in both summer and

winter for the orchards at Groblersdal, which is in agreement with other reports in

citrus (e.g., Kalma and Stanhill, 1969; Green and Moreshet, 1979; Allen et al., 1998).

The Kt values established for the ‘Rustenburg’ Navels are significantly higher in

winter than what was observed during the summer. Similar trends were reported by

García Petillo and Castel (2007) in Uruguay and Villalobos et al. (2013) in Spain.


75

'Bahianinha' Navel

Date

01

-Se

p-0

9

01

-Oct-

09

31

-Oct-

09

30

-No

v-0

9

30

-De

c-0

9

29

-Ja

n-1

0

28

-Fe

b-1

0

30

-Mar-

10

29

-Ap

r-1

0

29

-May-1

0

28

-Ju

n-1

0

28

-Ju

l-1

0

Kt

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

'Delta' Valencia

31

-Ju

l-08

30-A

ug-0

8

29-S

ep-0

8

29

-Oct-

08

28

-No

v-0

8

28

-De

c-0

8

27

-Ja

n-0

9

26

-Fe

b-0

9

28

-Ma

r-0

9

27-A

pr-

09

27

-Ma

y-0

9

26

-Ju

n-0

9

26

-Ju

l-09

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

13

-Au

g-1

0

12

-Se

p-1

0

12

-Oct-

10

11

-No

v-1

0

11

-De

c-1

0

10

-Ja

n-1

1

09

-Fe

b-1

1

11

-Mar-

11

10

-Ap

r-1

1

10

-May-1

1

09

-Ju

n-1

1

09

-Ju

l-1

1

08

-Au

g-1

1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4'Rustenburg' Navel

Figure 3.3. Transpiration coefficients (Kt) determined for the ‘Delta’ Valencia,

‘Bahianinha’ Navel and ‘Rustenburg’ Navel orchards.


76

'Delta' Valencia

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Kt

Kcb (FAO56)

'Rustenburg' Navel

Month

Au

gu

st

Se

pte

mb

er

Octo

be

r

No

ve

mb

er

De

ce

mb

er

Ja

nu

ary

Fe

bru

ary

Ma

rch

Ap

ril

Ma

y

Ju

ne

Ju

ly

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

'Bahianinha' Navel

Kt

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 3.4. Average monthly transpiration coefficients (Kt) for the three orchards.

Also shown are the FAO-56 standardised basal crop coefficients (Kcb

FAO-56) for a citrus orchard with 70 % canopy cover (‘Delta’ and

‘Rustenburg’ orchards) and 50 % ground cover (‘Bahianinha’ orchard),

all with no active ground cover, as given by Allen and Pereira (2009).


77

Table 3.4. Average transpiration crop coefficients (Kt) and water vapour pressure

deficit (VPD) for the summer and winter seasons in the three orchards.

Orchard Kt VPD (kPa)

Summer Winter Summer Winter

‘Delta’ Valencia 0.43 0.38 1.37 1.16

‘Bahianinha’ Navel 0.35 0.28 1.47 0.98

‘Rustenburg’ Navel 0.31 0.71 2.24 0.74

The most obvious difference in Kt values between orchards was found in the winter

months, where values were considerably higher in the winter rainfall region, which is

most likely attributable to the lower average vapour pressure deficit (VPD) (Table

3.4) and higher average transpiration rates at this time in this region (Table 3.2).

Kriedemann and Barrs (1981) and Oguntunde et al. (2007) both reported that VPD is

the dominant regulator of transpiration in citrus, when trees are well watered, with

transpiration decreasing with an increase in VPD. The lower VPD was also reflected

in lower ETo in winter (Table 3.2) in the winter rainfall region than in the summer

rainfall region.

A logical explanation for the trend of Kt values in the three orchards is that as ETo

increases during the summer months, tree transpiration does not increase at the

same rate. Figure 3.2 suggests that the transpiration measured in both orchards

does not always increase in proportion to the increase in ETo. This suggests that

there is a maximum transpiration rate for these citrus orchards, which is reached

when ETo exceeds approximately 5 mm day-1. The maximum transpiration rate for

the ‘Delta’ Valencia orchard is approximately 3 mm day-1, in the ‘Bahianinha’ Navels

approximately 2 mm day-1 and approximately 2.5 mm day-1 in the ‘Rustenburg’

Navels. The limited response to high ETo values is more apparent when one

considers the sharp responses that occur when ETo falls to low values in the three

orchards (Figure 3.2). The limited responses to high ETo is despite the fact that trees


78

are actively growing (in terms of flushes) and they have growing fruit on them. This is

suggestive of the fact that citrus trees might only be able to supply a certain

maximum amount of water to the canopy, irrespective of the atmospheric demand,

as highlighted by Sinclair and Allen (1982).

Kriedemann and Barrs (1981) suggested that this could partly be explained by the

low root:shoot ratio of citrus and the poorly developed root hairs that are not capable

of supplying enough water to match atmospheric demand during the peak periods.

Rodriguez-Gamir et al. (2010) working in young Valencia orange trees also

confirmed that transpiration of citrus tree species is strongly influenced by the leaf to

root ratio. This regulation mechanism has also been associated with stomatal

closure under conditions of high atmospheric evaporative demand (Kaufmann, 1977;

Kriedemann and Barrs 1981; Sinclair and Allen, 1982; García Petillo and Castel,

2007).

The Kt values obtained in the three orchards are much lower than the standardised

values reported by Allen and Pereira (2009) (Figure 3.4). If standard values

published by Allen et al. (1998) were to be applied over the measurement period in

each orchard, transpiration would have been overestimated by 94 % in the ‘Delta’

Valencia orchard, 98 % in the ‘Bahianinha’ Navel orchard and 96 % in the

‘Rustenburg’ Navel orchard. The ranges of seasonal Kt coefficients in the three

orchards compare very well to the range of 0.2-0.7 by Villalobos et al. (2013).

3.4 Conclusions

Average daily transpiration in the three orchards ranged from 0.77 mm day-1 to 2.26

mm day-1 depending on canopy size, season and climate (summer versus winter

rainfall areas). Total seasonal transpiration for the two orchards in which

measurements covered an entire production season, i.e. ‘Delta’ Valencia and

‘Rustenburg’ Navel orchards were 682 mm and 672 mm, respectively. Transpiration

coefficients derived from the measured data were lower than the standardised

values published in the FAO56. Differences in Kt values obtained amongst the three

orchards, as well as compared to values from other growing regions, means that this

kind of information is of significance to the commercial growers on whose farms the


79

research was conducted. Such information is not always applicable and readily

transferrable to many other regions within South Africa or across citrus growing

regions of the world, or even for different seasons. This emphasizes the need to

develop a relatively simple method for estimating site-specific crop coefficients, in

order to improve water management. Sap flow-based measurements of transpiration

obtained in this study present a valuable data set for developing models of citrus

transpiration that can be used to extrapolate measured water use to other growing

regions of the world.


80

Chapter 4: Estimation of transpiration crop coefficients from ground cover and

height in citrus orchards

4.1 Introduction

Knowledge of crop water use is the fundamental basis for efficient irrigation water

management strategies. The term irrigation water management encompasses

activities such as irrigation systems planning, irrigation scheduling and issuing of

water rights/permits. Measurements undertaken to gather information of crop water

use are time consuming, expensive and require specialised expertise, which is not

always available. The high variability between different orchards and the perennial

nature of orchards exacerbates the difficulty in obtaining water use estimates for

orchard crops (Hoffman et al., 1982; Castel et al., 1987). Consequently a number of

crop water use models have been developed which have proved very useful in

extrapolating measured data and predicting crop water use under a range of

conditions.

The use of the dual crop factor approach (Allen et al., 1998) has proved very useful

in micro-irrigated orchards, with discontinuous canopies, as it allows the separate

estimation of transpiration and evaporation. However, in tree crops, a linear

relationship between the evapotranspiration from a short, smooth and uniform grass

surface and a tall, very rough, clustered orchard canopy may not always hold true

(Annandale and Stockle, 1994; Testi et al., 2004). This probably explains the large

variation in Kt values determined among the three citrus orchards in this study

(Chapter 3), as well as crop coefficients (Kc and Kcb) reported in other citrus orchards

across the different growing regions of the world (see Table 1.3). This means that Kc

values derived in one location may not be readily transferable to other locations,

which limits their extrapolation to different climatic zones, with different orchard

management practices.

In an attempt to make crop coefficients more transferrable between different

orchards, Allen and Pereira (2009) developed a procedure for estimating crop

coefficients where vegetation density and height varies between orchards. These

authors found that under such conditions, Kc and basal crop coefficient (Kcb) values


81

can be estimated more accurately by taking into account fraction of ground covered

or shaded by the vegetation, the height of the vegetation and the degree of stomatal

regulation under wet soil conditions. An adjustment can also be made for climate by

taking into account the average relative humidity and wind speed of the climate,

which accounts for the differences in roughness between the grass reference

surface and the tall orchard canopy. According to the authors the leaf resistance

term that accounts for stomatal regulation requires further investigation in order to

improve the accuracy of the method in orchards. The aim of this chapter was to

evaluate this procedure for the derivation of orchard specific Kt values in three citrus

orchards in different climatic regions of South Africa (summer and winter rainfall

regions), by comparing derived Kt values with actual Kt values determined from

transpiration measurements using sap flow. It was hypothesized that a dynamic

estimate of leaf resistance is needed to predict daily and seasonal changes of

transpiration in citrus orchards.

4.2 Materials and Methods

The long-term transpiration measured in the ‘Delta’ Valencia, ‘Bahianinha’ and

‘Rustenburg’ Navel orchards was used together with weather data that was

measured simultaneously at the site to determine transpiration crop coefficients (Kt).

Transpiration crop coefficients, as suggested by Villalobos et al. (2013), were chosen

as Kcb includes some evaporation when the soil surface is dry and only transpiration

was measured in this study. Details of the three orchards and the measurement of

transpiration are given in Section 2.2.4.1 and 3.2.2. Measurement of weather

variables and determination of reference evapotranspiration (ETo) were presented in

Section 3.2.3.

4.2.1 Model description

Allen and Pereira (2009) published a method of estimating orchard specific crop

coefficients from measurements of effective ground cover and tree height.

In drip-irrigated orchards the Kt coefficients, which correlate with transpiration of

planted trees, can be expressed in terms of a density coefficient (Kd) as:


82

𝐾𝑡 = 𝐾𝑐 𝑚𝑖𝑛 + 𝐾d(𝐾t full − 𝐾𝑐 𝑚𝑖𝑛) Equation 4.1

where Kt is an approximation for transpiration crop coefficients for conditions

represented by the density coefficient, Kd; Kt full is the transpiration coefficient during

peak plant growth for conditions having nearly full ground cover (or LAI > 3) and Kc

min is the minimum crop coefficient for bare soil. The Kc min was set to zero, as only

transpiration from the trees measured using the heat ratio method sap flow

technique was considered.

The basal crop coefficients calculated following this approach apply to standard

conditions as stipulated in the FAO56 publication. As such it is recommended that

crop coefficients be adjusted for climates with minimum relative humidity (RHmin)

greater than or less than 45 % and/or with mean wind speeds at 2 m over grass (u2)

that are more or less than 2.0 m s-1. According to Allen et al. (1998) for large stand

size (greater than about 500 m2), Kt full for use with ETo can be approximated as a

function of mean plant height and adjusted for climate as:

𝐾t full = 𝐹r (min(1.0 + 0.1ℎ, 1.20) + [0.04(𝑢2 − 2) − 0.004(𝑅𝐻min − 45)] (ℎ

3)

0.3

)

Equation 4.2

where Fr [0-1] is a relative adjustment factor for stomatal control and h is the mean

maximum plant height (m) during the mid-season period, or full cover period.

Parameter Fr applies a downward adjustment (Fr ≤ 1.0) if the vegetation exhibits

more stomatal control on transpiration than is typical of most annual agricultural

crops, a situation that is typical of citrus (Kriedemann and Barrs, 1981).

Allen and Pereira (2009) suggested the following calculation for Fr for full cover

vegetation, based on the FAO Penman-Monteith equation and assuming full cover

conditions:

𝐹𝑟 ≈∆+𝛾(1+0.34𝑢2)

∆+𝛾(1+0.34𝑢2𝑟𝑙

100) Equation 4.3

where rl is the mean leaf resistance (s m-1); ∆ is the slope of the saturation vapour

pressure versus air temperature curve (kPa °C-1) and γ is the psychrometric constant

(kPa °C-1).


83

The density factor (Kd) was determined according to Allen and Pereira (2009) as

follows:

𝐾d = min (1, 𝑀𝐿𝑓c eff, 𝑓c eff

(1

1+ℎ)) Equation 4.4

where ƒceff is the effective fraction of ground covered or shaded by vegetation [0.01-

1] near solar noon, ML is a multiplier of ƒceff describing the effect of canopy density

on shading and on maximum relative evapotranspiration per fraction of ground

shaded [1.5-2.0], with a value of 1.5 recommended for citrus (Allen and Pereirra,

2009).

Effective fraction cover was calculated as the ratio of tree canopy width to inter-row

spacing or the ratio of ground shaded area by the crop at solar noon to the total area

available to the tree, following Allen et al. (1998) in the ‘Delta’ Valencia orchard with

a north-south orientation. In the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards,

provision had to be made for row orientation. In these orchards, ƒc eff was calculated

according to Allen et al. (1998) as follows:

ƒ𝑐 eff =ƒ𝑐

sin (𝛽) ≤ 1 Equation 4.5

where ƒc is the observed fraction of soil surface that is covered by vegetation as

seen from directly overhead. ƒc eff is usually calculated at solar noon, such that β

(mean elevation angle of the sun above the horizon during the period of maximum

evapotranspiration) can be calculated as:

𝛽 = arcsin [sin (𝜑)sin (𝛿) + cos (𝜑)cos (𝛿)] Equation 4. 6

where φ is latitude and δ is solar declination in radians. The average ƒc eff values

determined during the measurement period were 0.63, 0.61 and 0.88 for the ‘Delta’

Valencia, ‘Bahianinha’ and ‘Rustenburg’ Navel orchards, respectively.

4.2.2 Model calibration

Model calibration consisted of establishing parameters which provided for minimal

differences from measured Kt values on a monthly basis in all the orchards. Initially

the parameters recommended by Allen and Pereira (2009) for a generic citrus


84

orchard were used to estimate Kt values in the study orchards. Average monthly

values of rl were then estimated by inverting Equation 4.4, after solving for Fr by

inverting Equation 4.3, using known monthly values of Kt full. Average monthly rl

values were determined based on the daily values and used to estimate Kt.

Measurements of leaf resistance in the ‘Rustenburg’ Navel orchard were performed

with a SC-1 leaf porometer (Decagon Device Inc, Pullman, WA, USA) on 5 sunlit

leaves per tree instrumented with sap flow equipment. Measurements were made

every hour from sunrise to sunset for a minimum of 3 days and an average was

obtained for each measurement period.

4.2.3 Model validation

Monthly Kt coefficients developed using the different approaches were used to

estimate transpiration in each orchard. The performance of the model was tested by

comparing the predicted and observed transpiration values. The statistical

parameters used to test the goodness of fit for the model were the coefficient of

determination (R2), root mean square error (RMSE) and mean absolute error (MAE)

(de Jager, 1994). The total error of estimating water use over the season was also

considered.

4.3 Results and discussion

Transpiration coefficients determined using the parameters given by Allen and

Pereira (2009) (Kt Allen and Pereira) were higher than the measured Kt values in the three

orchards (Figure 4.1). The overestimation of transpiration coefficients and crop water

use using the given citrus parameters is likely a reflection of the greater stomatal

control of transpiration in citrus than in most other crops, which is attributed to high

resistances to water transport within the plant (van Bavel et al. 1967; Kriedemann

and Barrs 1981; Sinclair and Allen 1982). Whilst Allen and Pereira (2009) account for

this by including their Fr parameter, which is used as a downward adjustment on

crop coefficients for crops which exhibit more stomatal control on transpiration than

most other agricultural crops, the rl value of 420 s m−1 suggested by the authors may

be too low, especially during hot summer months, when VPD increases.


85

'Delta' Valencia

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Kt measured

Kcb FAO56

Kt Allen & Pereira

Kt monthly avg. rl

Kt rl(ETo)

'Rustenburg' Navel

Month

Au

gu

st

Se

pte

mb

er

Octo

be

r

No

ve

mb

er

De

ce

mb

er

Ja

nu

ary

Fe

bru

ary

Ma

rch

Ap

ril

Ma

y

Jun

e

Ju

ly

0.2

0.4

0.6

0.8

1.0

'Bahianinha' Navel

Kt

0.2

0.4

0.6

0.8

1.0

Figure 4.1. Derived monthly transpiration crop coefficients (Kt) for the three

orchards. Transpiration crop coefficients were determined using

measured transpiration (Kt measured), the method described in Allen and

Pereira (2009) using the parameters given for citrus (Kt Allen and Pereira),

using estimates of monthly average rl values from transpiration data (Kt

monthly avg. rl) and using rl estimated from the relationship with ETo (Kt rl

(ETo)). Also shown are FAO-56 standardised basal crop coefficients

(Kcb FAO-56) for a citrus orchard with 70% canopy cover (‘Delta’ and

‘Rustenburg’ orchards) and 50% ground cover (‘Bahianinha’ orchard),

all with no active ground cover, as given by Allen and Pereira (2009)


86

More appropriate values for rl were therefore estimated following a procedure

recommended by Allen and Pereira (2009), using measured transpiration data.

Following their approach rl values were estimated by inverting Equation 4.3, after

solving for Fr by inverting Equation 4.2 using known values of Kt full. Monthly, Kt full

values were obtained by scaling measured monthly Kt values with the appropriate Kd

value and were used to calculate a mean monthly rl (Figure 4.2). There was a very

good agreement between measured Kt values (Kt measured) estimated using the

calculated rl values (Kt monthly avg. rl) (Figure 4.1) with the two plots sitting perfectly on

top of one another. The perfect similarity between the measured and estimated Kt

values is expected since there is a high level of circularity involved in the estimation

process.

Month

August

Septe

mber

Octo

ber

Novem

ber

Decem

ber

January

Febru

ary

Marc

h

April

May

June

July

Me

an

lea

f re

sis

tance

(s m

-1)

0

1000

2000

3000

4000

'Delta' Valencia

'Bahianinha' Navels

'Rustenburg' Navels

Average

Allen and Pereira (2009)

Stomatal resistance measured in 'Rustenburg' Navels

Figure 4.2. Monthly mean leaf resistances calculated following the procedure

outlined by Allen and Pereira (2009), compared with the values

suggested by Allen and Pereira (2009) for citrus and daily stomatal

resistance measure in the ‘Rustenburg’ Navel orchard in Citrusdal.


87

It is the magnitude and trend of rl values estimated following this method suggested

by Allen and Pereira (2009) that are of interest in as far as this result is concerned.

The rl values estimated in the three orchards ranged from 419 to 2 694 s m-1, which

is higher than the values suggested by Allen and Pereira (2009). Although Allen and

Pereira (2009) emphasised that the values of rl obtained using this procedure should

only be used in the estimation of Fr, these values were not too dissimilar to published

stomatal resistance data for citrus. Stomatal resistances in Shamouti orange varied

between 500 and 2000 s m-1 (Cohen and Cohen 1983); in young Navel orange trees

they varied between 200 to 8280 s m-1 (Dzikiti et al., 2007) and in oranges 295 and

830 s m-1 (Pérez-Pérez et al., 2008). The rl values in Figure 4.2 may therefore be

reasonable, and may not be heavily biased by the procedure outlined by Allen and

Pereira (2009), indicating that measured leaf resistances could potentially be used to

derive crop coefficients. However, average daily stomatal resistance, measured in

the various citrus orchards in Citrusdal, was between 300 and 1 000 s m−1 (Figure

4.2), which was considerably lower than the rl values of between 530 and 2,694 s

m−1 for this period, but generally the trend was very similar. Contrary to a constant

value of 420 s m-1, suggested by Allen and Pereira (2009), the average rl values

increased during the summer months in all three orchards. The increase in rl values

during the summer months, which are characterised by high atmospheric

evaporative demands, is evidence of strong stomatal control of transpiration in citrus.

The accurate estimation of Kt values and subsequent prediction of transpiration in

the three orchards using the method of Allen and Pereira (2009) hinged on the back-

calculation of rl. It is the estimation of mean rl, without measured transpiration, that

really hinders the ease with which this approach can be used to accurately estimate

crop coefficients for different citrus orchards. An independent methodology for

estimating this parameter was therefore sought by the parameterization of a

relationship between rl and routinely measured weather variables such as relative

humidity, VPD or ETo. A simple reproducible relationship with an excellent coefficient

of determination (R2 = 0.97) was found for the Citrusdal site during the 2010/11

season between rl and ETo (Figure 4.3).


88

Reference evapotranspiration (mm day-1

)

0 2 4 6 8 10

Mean leaf re

sis

tance (

s m

-1)

0

500

1000

1500

2000

2500

3000

y = 316x - 61

R2 = 0.97

Figure 4.3. Relationship between reference evapotranspiration (ETo) and mean leaf

resistance for the ‘Rustenburg’ Navel orchard

Monthly transpiration estimates obtained in all the orchards, using the relationship

between ETo and rl, are presented in Figure 4.4. In the ‘Delta’ Valencia and

‘Bahianinha’ orchards, transpiration was underestimated at the beginning of the

season and overestimated at the end of the season. The underestimation at the start

of the season was more pronounced in the ‘Delta’ Valencia orchard, whilst the

overestimation at the end of the season was more pronounced in the ‘Bahianinha’

Navel orchard. In the ‘Rustenburg’ Navel orchard, in the 2010/11 season, good

estimates of water use were obtained throughout the season. The performance of

the model, as determined by statistical parameters, was good in the orchard in

Citrusdal, as the MAE was <20 % and D greater than 0.8. It did not, however,

perform as well in the orchards in the summer rainfall region with an MAE of 23 and

24 % and D of 0.55 and 0.63.


89

'Delta' Valencia

0

20

40

60

80

100

Measured

Estimated

'Bahianinha' Navel MAE = 23 %RMSE = 14.9 mm

D = 0.55

Mo

nth

ly t

ransp

ira

tio

n (

mm

)

0

10

20

30

40

50

60

70

'Rustenburg' Navel

Month

Au

gu

st

Se

pte

mb

er

Octo

ber

No

ve

mb

er

De

ce

mb

er

Ja

nua

ry

Fe

bru

ary

Ma

rch

Ap

ril

Ma

y

Ju

ne

Ju

ly

0

20

40

60

80MAE = 5 %

RMSE = 3.7 mmD = 0.99

MAE = 24 %RMSE = 15.7 mm

D = 0.63

Figure 4.4. Monthly measured and estimated transpiration using Kt values derived

from mean leaf resistance, estimated from the relationship between

reference evapotranspiration and mean leaf resistance in the three

orchards. Statistical parameters shown include mean absolute error

(MAE), root of the mean square error (RMSE) and index of agreement

(D)


90

Cumulative transpiration for the measurement periods was underestimated by 0.1 %

in the ‘Rustenburg’ Navels, and overestimated by 9 % in the ‘Delta’ Valencia orchard

and 18 % in the ‘Bahianinha’ Navel orchard when using the estimated Kt values (Kt rl

(ETo) (Figure 4.5). Given the empirical nature, the performance was fairly good,

especially compared to using the parameters stipulated by Allen and Pereira (2009)

for citrus. If derived Kt values using the parameters stipulated by Allen and Pereira

(2009), were to be applied over the measurement periods, they would have resulted

in a 139 % over-estimation of transpiration in the ‘Delta’ Valencia orchard, a 172 %

over-estimation in the ‘Bahianinha’ Navel orchard and a 95 % over-estimation in the

‘Rustenburg’ Navel orchard (Figure 4.5).

The accuracy of using the method of Allen and Pereira (2009) coupled with a

relationship between rl and ETo provided seasonal estimates within an acceptable

error range. This method could therefore be used for irrigation planning purposes

and for the issuing of water permits. However, the inability to predict water use

accurately on a monthly basis for most of the season limits the use of this procedure

for irrigation scheduling, which will require more reliable estimates of rl. This is not

unexpected, as stomatal conductance is known to be regulated by a number of

factors, which includes solar irradiance, ambient CO2 concentration, leaf to air water

vapour pressure deficit, leaf temperature, leaf water status and hydraulic limitations

to leaf water supply (Jarvis 1976; Sperry et al., 2002), and it is usually a combination

of these factors that determines stomatal conductance. This creates uncertainty

when only using climatic data to predict stomatal responses. In this respect, reduced

sink activity or accumulation of carbohydrates in leaves could also lead to decreases

in stomatal conductance (Iglesias et al., 2002; Syvertsen et al., 2003; Duan et al.

2008), which may be a contributing factor to the increased leaf resistance in the

Groblersdal orchards at the end of the season, as both these orchards experienced

lower than average yields during the monitoring period. As a result of the reduced

number of fruit on trees, and therefore sink strength, feedback inhibition of

photosynthesis through carbohydrate accumulation in leaves may have occurred.

Although Nebauer et al. (2013) attributed the lack of difference in photosynthetic

rates between high and low-yielding citrus trees, in alternate bearing cycles, to an

unsaturable sink in the root system of perennial fruit trees, their evidence is not


91

compelling enough to suggest that changes in fruit load have no impact on overall

tree sink demand and canopy conductance. Further research is therefore required to

determine the relationship between yield and water use, as this has implications for

predicting seasonal water use. The solution for better prediction of leaf resistances

may be to use more mechanistic models which can predict canopy conductance

based on canopy size, environmental variables and sink strength or potential yield.

Similar approaches have been undertaken by Oguntunde et al. (2007) and Villalobos

et al. (2009, 2013) and have shown some promise, but the ability of these models to

predict citrus water use need to be verified in orchards with different canopy sizes

and in different climatic regions.


92

'Delta' Valencia

0

200

400

600

800

1000

1200

1400

1600

1800

2000

ETo

Transpiration (Allen and Pereira)

Measured transpiration

Transpiration Kt rl (ETo)

'Bahianinha' Navel

Cum

mula

tive E

To

and T

ranspiration (

mm

)

0

200

400

600

800

1000

1200

1400

'Rustenburg' Navel

Date

August

Septe

mber

Octo

ber

Novem

ber

Decem

ber

Jan

uary

Feb

ruary

Marc

h

April

May

Jun

e

July

August

0

200

400

600

800

1000

1200

1400

1600

1800

Figure 4.5. Cumulative ETo, measured transpiration and transpiration estimated

from the derived crop coefficients in the ‘Delta’ Valencia orange orchard

(1 August 2008 to 31 July 2009), the ‘Bahianinha’ Navel orchard (3

September 2009 to 30 June 2010) and the ‘Rustenburg Navel orchard

(13 August 2010 to 12 August 2011)


93

4.4 Conclusions

The development of transpiration coefficients from ground cover and crop height

published by Allen and Pereira (2009) was evaluated. Due to the greater stomatal

control of transpiration in citrus than in most other crops, crop coefficients that are

constant or are based on parameters that are constant are not suitable for accurate

predictions of water use, as crop coefficient models assume atmospheric demand-

limited conditions and transpiration in citrus is often water-supply limited, even in

well-watered orchards. Good agreement between measured and predicted

transpiration was obtained by using leaf resistances back-calculated from the

measured transpiration coefficient values. A relationship between monthly reference

evapotranspiration and mean leaf resistance provided a means of estimating a

dynamic leaf resistance which gives crop coefficients with a reasonable degree of

accuracy.


94

Chapter 5: Predicting transpiration of citrus orchards using the Penman-

Monteith equation coupled with a Jarvis-type multiplication canopy

conductance model

5.1 Introduction

Transpiration coefficients determined according to Allen and Pereira (2009), based

on ground cover and crop height and using a dynamic estimate of leaf resistance,

provided good seasonal estimates of transpiration, but could not provide reasonable

monthly estimates throughout the season (Chapter 4). The leaf resistances

calculated using the measured transpiration data were higher than that suggested by

Allen and Pereira (2009) for citrus. This reiterates the strong stomatal control over

transpiration that has been reported in citrus (Kriedemann and Barrs, 1981; Meyer

and Green, 1981; Sinclair and Allen, 1982). A mechanistic approach that

incorporates the intra-annual dynamics of canopy conductance may therefore hold

the solution for improved modelling and/or simulation of citrus transpiration

(Villalobos et al., 2013; Taylor et al., 2015).

When measurements of transpiration are available, the bulk canopy conductance of

a vegetated surface can be obtained using the top-down approach by inversion of

the Penman-Monteith equation (Baldocchi et al., 1991). Such data sets have been

used to develop canopy conductance models, as a function of environmental

variables, for predicting transpiration using the Penman-Monteith equation (e.g.,

Granier and Loustau 1994; Green and McNaughton 1997; Zhang et al., 1997;

Oguntunde et al., 2007; Villalobos et al., 2009; Villalobos et al., 2013). Jarvis-type

models, i.e. multiplicative models of similar form to that originally proposed by Jarvis

(1976), have been parameterised using weather variables to model the variations in

canopy conductance with satisfactory accuracy in a number fruit trees e.g., olives

(Villalobos et al., 2000; Testi et al., 2006), cashew (Oguntunde and van de Giesen,

2005) and citrus (Cohen and Cohen, 1983; Oguntunde et al., 2007).

Besides being based on strong physiological relationships between stomatal

responses and environmental variables, the other advantage of the Jarvis model

(Jarvis, 1976) is that weather data available from a standard automatic weather


95

station is used to predict canopy conductance. This approach therefore does not

require any additional input data than what is required for the FAO56 approach.

Whilst the use of the Penman-Monteith equation coupled with a Jarvis-type

conductance model by Oguntunde et al. (2007) in citrus showed some promise, it

was only evaluated for a short period of time in a single orchard. Whitley et al. (2009)

showed that the Penman-Monteith equation coupled with the Jarvis model with a

single set of parameters was able to accurately predict transpiration in a forest

species over an annual cycle. The ability of this approach, to estimate long-term

transpiration in citrus and its transferability amongst orchards with varying canopy

sizes and in different climatic regions, still needs to be verified.

The aims of this study were to: (i) Use sap flow-based transpiration measurements to

parameterise a Jarvis-type conductance model for inclusion in the Penman-Monteith

equation for predicting long-term transpiration of citrus orchards and (ii) To test the

transferability of the parameters of a Jarvis-type model obtained in an orchard in the

summer rainfall area to predict transpiration in orchards situated in the summer and

winter rainfall areas of South Africa. The hypothesis that a dynamic estimate of

canopy conductance is needed to predict daily and seasonal changes of

transpiration in citrus orchards was further tested.


Long-term orchard transpiration and weather data measurements that were

conducted in the ‘Delta’ Valencia, ‘Bahianinha’ and ‘Rustenburg’ Navel orchards

were used in the modelling approach conducted in this chapter. Details of the

measurement of long-term transpiration and weather parameters are given in

Chapters 2 and 3. The weather parameters used included wind speed, solar

radiation, air temperature and relative humidity.

5.2.1 Calculation of canopy conductance

Bulk canopy conductance (gc) was calculated from transpiration measurements

using the inversion of the following Penman-Monteith equation (Monteith and

Unsworth, 1990):


96

𝜆𝐸𝑐 =∆(𝑅𝑛−𝐺)+𝜌𝑎𝐶𝑝𝑔𝑎𝑉𝑃𝐷

∆+𝛾(1+𝑔𝑎𝑔𝑐

) Equation 5. 1

where λ is the latent heat of vaporization of water (J kg-1), Ec is canopy transpiration

(kg m-2 s-1), Δ is slope of the water vapour pressure curve versus temperature (kPa

K-1), Rn is net irradiance at the crop surface (W m-2), G is soil heat flux (W m-2), taken

as 10 % of Rn, ρa is the density of dry air (kg m-3), Cp is the specific heat capacity of

the air (J kg-1 K-1), VPD is saturation vapour pressure deficit (kPa), γ is the

psychrometric constant (kPa K-1), ga is the aerodynamic conductance (m s-1) and gc

is the canopy conductance (m s-1). Rn was estimated from solar irradiance measured

at the automatic weather stations according to Allen et al. (1998) using

measurements of citrus reflection coefficient obtained using an albedometer in the

‘Delta’ Valencia orchard.

Leaf boundary conductance (ga) was calculated from an empirical relation derived by

Landsberg and Powell (1973), which accounts for the mutual sheltering of clustered

leaves as:

𝑔𝑎 = 0.172𝑝−0.56 (𝑢

𝑑)

0.5

Equation 5. 2

where d is a characteristic leaf dimension, equal to 8 mm for citrus leaves (Dzikiti et

al., 2011), u is the mean wind speed (m s-l ) across the leaf surface, and p is a

measure of foliage density to wind given by the ratio of total leaf plane area to the

area of the foliage projected onto a vertical plane. Leaf area was determined using a

leaf area density of 2.5 m2 m-3 and tree canopy volume was determined according to

a cone shape following Annandale et al. (2003).

5.2.2 Modelling canopy conductance

Canopy conductance was modelled using a Jarvis-type multiplicative model (Jarvis

1976), similar to the one used by Oguntunde et al. (2007), on an hourly basis with

weather data as follows:

𝑔𝑐,𝑗 = 𝑔𝑐 𝑚𝑎𝑥ƒ(𝑆𝑅)ƒ(𝑉𝑃𝐷)ƒ(𝑇) Equation 5.3

where gc,j is the canopy conductance predicted by the Jarvis model, gc max is the

maximum canopy conductance (m s-1), ƒ(SR) is a function of solar radiation, ƒ(VPD)

is a function of water vapour pressure deficit and ƒ(Ta) is a function of air


97

temperature. The functions have values ranging between 0 and 1. A response

function for soil water content has been included in the Jarvis-type model in some

studies, particularly native forests (e.g. Whitley et al. 2008), but as the orchards in

this study were well-irrigated this function was set to one. The control functions of air

temperature and solar irradiance were similar to those of Oguntunde et al. (2007)

and took the following forms:

ƒ(𝑆𝑅) =𝑆𝑅

𝑅𝑚(

𝑅𝑚+𝑘𝑅

𝑆𝑅+𝑘𝑅) Equation 5. 4

ƒ(𝑇𝑎) =(𝑇𝑎−𝑇𝐿)(𝑇𝐻−𝑇𝑎)𝑡

(𝑘𝑇−𝑇𝐿)(𝑇𝐻−𝑘𝑇) Equation 5.5

𝑡 =𝑇𝐻−𝑘𝑇

𝑘𝑇−𝑇𝐿 Equation 5.6

where kR and kT are model parameters for the respective functions in which they are

used, TL and TH are the lower and upper temperature limits to transpiration fixed at 0

and 45 oC, respectively (Wright et al., 1995; Oguntunde et al., 2007). Rm is an

arbitrary radiation constant, often fixed at 1000 W m-2 (e.g. Wright et al., 1995;

Sommer et al., 2002). For the control function for water vapour pressure deficit the

equation derived by Zhang et al. (1997) was used. The equation is stated as:

ƒ(𝑉𝑃𝐷) =1+𝑘𝐷1𝑉𝑃𝐷

1−𝑘𝐷2𝑉𝑃𝐷 Equation 5.7

where kD1 and kD2 are model parameters.

5.2.2.1 Model parameterisation

Parameters gc max, kR, kT, kD1 and kD2 were optimised by minimising the sum of

squares of the residuals of the measured and modelled canopy conductance as:

𝑆2(𝑘) = ∑ (𝑔𝑐𝑖 − 𝑔𝑐𝑗(𝑘, 𝑥𝑖))𝑛𝑖=1 Equation 5. 8

where gci is the ith value of canopy conductance calculated using transpiration data

by inverting Equation 5.1, gc,j is the corresponding canopy conductance value

predicted by the Jarvis model, k represents the model parameters (kR, kT, kD1 and

kD2) and xi is the input variables of the ith model value. Minimisation of S2 was carried


98

out by optimising k using the Marquardt and Simplex iterative procedures in the

ModelMaker 3rd Edition software package (Cherwell Scientific Publishing Ltd, UK).

Days with the highest gc values (10 to 15 December 2008) were used.

5.2.2.2 Model validation

Validation of the model was performed by calculating canopy conductance using the

optimised parameters of the Jarvis model and using these values in the Penman-

Monteith equation to estimate hourly transpiration. Only transpiration values for the

day-time (0800 h to 1700h) period were used to evaluate the performance of the

model. These values were compared to the day-time transpiration measured using

the HRM technique from16 December 2008 to 26 June 2009, to assess the ability of

the model to predict long-term transpiration in the ‘Delta’ Valencia orchard.

The transferability of the parameters optimised in the ‘Delta’ Valencia orchard was

evaluated in a ‘Bahianinha’ Navel orchard at the same location and in a ‘Rustenburg’

Navel orchard in the winter rainfall area of South Africa. Maximum canopy

conductance (gc max) required in Equation 5.3 was calculated for these orchards

according to Whitehead (1998), which was also used by Whitely et al. (2009):

𝑔𝑐 𝑚𝑎𝑥 = 𝐿𝐴𝐼 × 𝑔𝑠 𝑚𝑎𝑥 Equation 5. 9

where LAI is leaf area index and gs max is the maximum stomatal conductance. LAI in

the three orchards was measured using an AccuPAR Ceptometer (model LP-80

Decagon Devices, Inc, Pulman, WA, USA). The gc max, estimated through the

optimisation process based on the gc data calculated by inverting the Penman-

Monteith equation in the ‘Delta’ Valencia orchard, was used to determine gs max for

citrus using the LAI of the orchard. The response parameters of the weather

variables (i.e. kR, kT, kD1 and kD2) were applied in their original forms, as determined

for the ‘Delta’ Valencia orchard.

5.2.3 Statistical analysis

The statistical parameters used to test the predicted values against the observed

data for the model are linear regression models, the coefficient of determination (R2),

root mean square error (RMSE), mean absolute error (MAE) and the index of


99

agreement of Willmott (D) (de Jager, 1994). The model reliability criteria

recommended by de Jager (1994) are that R2 should be greater than 0.5, D should

be greater than 0.8 and MAE should be less than 20 %.

5.3 Results

5.3.1 Canopy conductance

A typical diurnal trend of gc in the ‘Delta’ Valencia orchard, calculated from the

inversion of the Penman-Monteith equation on a clear sky day (27 January 2009),

and weather variables are presented in Figure 5.1. The gc on this particular day

reached a maximum value of 5.7 m s-1 in the morning (0800 to 1100 h) and gradually

decreased to a minimum value of 1.9 mm s-1 at 1500 h. The high gc in the morning is

in response to an increase in solar irradiance, which causes a sudden increase in

the VPD on the evaporating leaf surface; whilst later on in the day the responses of

gc are controlled by a combination of variables VPD, SR, and Ta. This trend of high

and low values of gc in the early morning and late afternoon, which was observed on

most clear-sky days, is consistent with measurements of stomatal conductance of

citrus (Cohen and Cohen, 1983).


100

00:00 04:00 08:00 12:00 16:00 20:00 00:00

VP

D (

KP

a)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Time

00:00 04:00 08:00 12:00 16:00 20:00 00:00

gc (

mm

s-1

)

0

1

2

3

4

5

6

Time

00:00 04:00 08:00 12:00 16:00 20:00 00:00

Ta (

oC

)

18

20

22

24

26

28

30

00:00 04:00 08:00 12:00 16:00 20:00 00:00

SR (

W m

-2)

0

200

400

600

800

1000

1200

A

B

C

D

Figure 5.1. Typical diurnal trend of A) solar irradiance (SR), B) air temperature (T),

C) vapour pressure deficit (VPD) and D) canopy conductance (gc),

calculated from the inversion of the Penman-Monteith, in the ‘Delta’

Valencia orchard on a clear sky day, 27 January 2010.

Considerable scatter, signifying the stomatal response to weather variables, is

exhibited by the gc values when plotted over the measurement period in each

orchard (Figure 5.2). The gc values show a similar trend in the ‘Delta’ Valencia and

‘Bahianinha’ Navel orchards, where the highest values were observed in summer

and lowest values were at the end of the winter months. The highest gc values

recorded in the ‘Delta’ Valencia and ‘Bahianinha’ Navel orchards were approximately

12 mm s-1 and 9 mm s-1, respectively. In contrast, maximum canopy conductance

(10 mm s-1) in the ‘Rustenburg’ Navels orchard remained relatively constant

throughout the measurement period.


101

Figure 5.2. Hourly canopy conductance (gc) calculated using the measured

transpiration and inverting the Penman-Monteith equation in the three

orchards. Gaps in the plotted data were due to missing hourly weather

data caused by power failure to the weather stations.

'Delta' Valencia

'Bahianinha' Navel

'Rustenburg' Navel


102

5.3.2 Parameterisation of the Jarvis model

The five parameters, i.e. gc max, kD1, kD2, kT and kR, which describe the seasonal

response of canopy conductance to SR, VPD and Ta, obtained in the ‘Delta’ Valencia

orchard through the Marquardt and Simplex iterative procedures on an hourly basis,

are shown in Table 5.1. A very good correlation, R2 value of 0.97, was observed

between the measured and predicted canopy conductance during the optimisation

process in the ‘Delta’ Valencia orchard (Table 5.1). The three functions of SR, VPD

and Ta therefore explained over 97 % of the variation in canopy conductance in the

orchard and all parameter values were statistically significant (P<0.001). Figure 5.3

shows the normalised canopy conductance (gc/gc max) plotted against the functions of

weather variables (i.e. solar radiation; VPD and temperature) for the orchard. The

functional forms of the equations fit very well to the boundary regions described by

the data (Figure 5.3).

Table 5.1. Optimised parameters for the Jarvis model used to predict canopy

conductance with water vapour pressure deficit, solar irradiance and air

temperature as response functions in the ‘Delta’ Valencia orchard.

Parameter Value

gcmax (mm s-1) 14.0380

kD1 (kPa) 0.0477

kD2 (kPa) -0.1799

kT (oC) 18.6410

kR (W m-2) 350.1700

R2 0.9700

P value <0.0010


103

B

Water vapour pressure deficit (kPa)

0 1 2 3 4 5

gc/g

c m

ax

0.0

0.2

0.4

0.6

0.8

1.0

1.2

A

Solar irradiance (W m-2

)

0 200 400 600 800 1000 1200

0.0

0.2

0.4

0.6

0.8

1.0

1.2

C

Air temperature (oC)

0 10 20 30 40

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Figure 5.3. Normalised canopy conductance in the ‘Delta’ Valencia orchard plotted

against (A) solar radiation (B) vapour pressure deficit and (C)

temperature. The forms of the model functions, based upon the

optimised parameters, are shown as solid lines.


104

5.3.2 Predicting transpiration using the Penman-Monteith equation coupled

with the Jarvis-type model

Figure 5.4 shows the relation between the gc predicted by the Jarvis model and gc

obtained from sap flow data by inverting the Penman-Monteith equation. The

predicted values were scattered around the 1:1 line with a reasonable correlation (R2

= 0.56). There is high variance between predicted and measured values at higher

values of gc. Despite the disparities between measured and estimated hourly gc,

when using these values in the Penman-Monteith equation fairly good predictions of

the observed range of daily transpiration volumes were obtained (Figure 5.5A). Both

the day-to-day variation in transpiration and the gradual decline daily transpiration

rates as winter approached were captured by the model. Regression analysis

resulted in a slope of close to 1 (y = 1.13) between predicted and measured

transpiration in the ‘Delta’ Valencia orchard (Figure 5.5B) and the statistical

parameters were within the ranges stipulated for good model performance by de

Jager (1994).

y = 0.7783x

R2 = 0.56

Measured gc (mm s

-1)

0 2 4 6 8 10 12 14 16 18

Pre

dic

ted g

c (

mm

s-1

)

0

2

4

6

8

10

12

14

16

18

1:1 line



in the ‘Delta’ Valencia orchard.


105

A

Date

01

-De

c-0

8

01

-Ja

n-0

9

01

-Fe

b-0

9

01

-Ma

r-0

9

01

-Ap

r-0

9

01

-Ma

y-0

9

01

-Ju

n-0

9

01

-Ju

l-0

9

Tra

nspiration (

mm

day

-1)

0.0

0.5

1.0

1.5

2.0

2.5

Predicted

Measured

B

y = 1.13x

R2 = 0.69

MAE = 19.37 %

D = 0.89

RMSE = 0.09

0.0 0.5 1.0 1.5 2.0 2.5

Pre

dic

ted

tra

nsp

ira

tio

n (

mm

da

y-1

)

0.0

0.5

1.0

1.5

2.0

Measured transpiration (mm day-1

)

Figure 5.5. Measured and predicted daily transpiration in the ‘Delta’ Valencia

orchard for A) the period 16 December 2008 to 26 June 2009 and (B)

regression analysis. Statistical parameters include slope of regression

equation, coefficient of determination (R2), mean absolute error (MAE),

Willmot coefficient of agreement (D) and root mean square error

(RMSE). The missing data were due to missing hourly weather data

caused by power failure to the weather station.


106

Whilst the model performed very well in the ‘Delta’ Valencia parameterisation

orchard using independent validation data, it is important that the model is

transferable and can be used to predict long-term transpiration in a wide range of

citrus orchards. The transferability of the parameters for the Jarvis-type canopy

conductance model was therefore evaluated in a ‘Bahianinha’ Navel orchard at the

same location and in a ‘Rustenburg’ Navel orchard in the winter rainfall region of

South Africa. The value for gs max for the ‘Delta’ Valencia orchard was 4.92 mm s-1,

and was used together with orchard LAI to determine gc max in the ‘Bahianinha’ and

‘Rustenburg’ Navel orchards using Equation 5.9. Following this approach hourly gc

was poorly estimated in both of these orchards (Figure 5.6), with an R2 value of 0.47

for the ‘Bahianinha’ Navel orchard (Figure 5.6A) and 0.41 ‘Rustenburg’ Navel

orchard (Figure 5.6B). In the ‘Bahaininha’ Navel orchard gc tended to be

overestimated (slope = 1.34), whilst in the ‘Rustenburg’ Navel orchard gc tended to

be underestimated (slope = 0.64). As a result transpiration was overestimated in the

‘Bahianinha’ Navel orchard throughout the measurement period and underestimated

in the ‘Rustenburg’ Navel orchard (Figure 5.7). Three of the four statistical

parameters (i.e. MAE, D and RMSE) indicated that the parameters for the Jarvis-

type model determined in the ‘Delta’ Valencia orchard did not predict transpiration

adequately in both the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards (Figure 5.8).


107

'Bahianinha' Navel

1:1 line

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

14

'Rustenburg' Navel

Measured gc (mm s

-1)

0 2 4 6 8 10 12

Pre

dic

ted

gc (

mm

s-1

)

0

2

4

6

8

10

12

y = 1.34x

R2 = 0.47

y = 0.64x

R2 = 0.41

1:1 line

Figure 5.6. Relationship between gc predicted by the Jarvis model using

parameters of the ‘Delta’ Valencia orchard and gc obtained from sap

flow data by inverting the Penman-Monteith equation in the

‘Bahianinha’ and ‘Rustenburg’ Navel orchards.


108

'Rustenburg' Navel

Date

01

-Au

g-1

0

05

-Se

p-1

0

10

-Oct-

10

14

-No

v-1

0

19

-De

c-1

0

23

-Ja

n-1

1

27

-Fe

b-1

1

03

-Ap

r-1

1

08

-May-1

1

12

-Ju

n-1

1

17

-Ju

l-1

1

21

-Au

g-1

1

0.0

0.5

1.0

1.5

2.0

2.5

'Bahianinha' Navel

01

-De

c-0

9

21

-De

c-0

9

10

-Ja

n-1

0

30

-Ja

n-1

0

19

-Fe

b-1

0

11

-Mar-

10

31

-Mar-

10

20

-Ap

r-1

0

10

-May-1

0

30

-May-1

0

19

-Ju

n-1

0

Tra

nsp

ira

tio

n (

mm

)

0.0

0.5

1.0

1.5

2.0

Measured

Predicted

Figure 5.7. Time series of measured and predicted transpiration in the ‘Bahianinha’

and ‘Rustenburg’ Navel orchards using Jarvis parameters optimised in

the ‘Delta’ Valencia orchard.


109

'Rustenburg' Navel

Measured transpiration (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Pre

dic

ted

tra

nsp

ira

tio

n (

mm

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

y = 0.8123x

R2 = 0.59

MAE = 38.64D = 0.69

RMSE = 0.36

'Bahianinha' Navel

y = 1.2304x

R2 = 0.57

MAE = 28.79D = 0.73

RMSE = 0.33

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Figure 5.8. Regression analysis between measured and predicted transpiration in

the ‘Bahianinha’ and ‘Rustenburg’ Navel orchard using parameters

determined in the ‘Delta’ Valencia orchard. Statistical parameters used

include slope of regression equation, coefficient of determination (R2),

mean absolute error (MAE), Willmot coefficient of agreement (D) and

root mean square error (RMSE).

As transpiration was poorly predicted in the ‘Bahianinha’ and ‘Rustenburg’ Navel

orchards when using the parameters for the ‘Delta’ Valencia orchard, it was decided

to parameterise the Jarvis model in the ‘Bahianinha’ and ‘Rustenburg’ Navel

orchards following the same procedure as in the ‘Delta’ Valencia orchard.

Parameterisation of the Jarvis model was done using data measured during the


110

period of 3 to 9 December 2009 in the ‘Bahianinha’ Navel orchard; and 13 to 17

August 2010 in the ‘Rustenburg’ Navel orchard. A very good correlation (R2 >0.9)

was once again observed between the measured and predicted canopy conductance

during parameterisation, such that over 90 % of the variation in canopy conductance

in the two orchards was explained by the three functions of SR, VPD and Ta (Table

2). All parameter values were found to be statistically significant (P<0.001). Most of

the normalised canopy conductance data points were below the ideal situation

described by the functional forms in both the ‘Bahianinha’ Navel (Figure 5.9) and

Rustenburg Navel orchards (Figure 5.10).

Table 5.2. Parameters for the response functions of water vapour pressure deficit,

solar irradiance and air temperature for the Jarvis model determined

through the optimisation process in the ‘Bahianinha’ and ‘Rustenburg’

Navel orchards.

Parameter ‘Bahianinha’

Navel

‘Rustenburg’

Navel

gc max (mm s-1) 12.2970 18.0260

kD1 (kPa) 0.0503 0.0502

kD2 (kPa) -0.3083 -0.2673

kT (oC) 18.4871 19.3670

kR (W m-2) 363.2290 356.6990

R2 0.9900 0.9200

P value <0.0010 <0.0010

There were close similarities between the optimum parameters of the Jarvis-type

model obtained in the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards (Table 5.2) and

those of the ‘Delta’ Valencia orchard (Table 5.1). Maximum differences amongst the

kD1, kD2, kT and kR parameters in respect of the ‘Delta’ Valencia orchard parameters

for the three orchards were 8.6, 33.9, 4.8 and 11.2 %, respectively. There were also

differences in the values of gc max that were obtained during the optimisation process

(Table 5.2) and those calculated using Equation 5.9 for the two orchards. The gc max

values obtained for the different orchards seem to reflect the sizes of the tree

canopies as they increase with measured LAI.


111

Temperature (oC)

0 10 20 30 40

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Solar radiation (W m-2)

0 200 400 600 800 1000 1200

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Vapour pressure deficit (kPa)

0 1 2 3 4 5 6

gc/g

c m

ax

0.0

0.2

0.4

0.6

0.8

1.0

1.2

A

B

C

Figure 5.9. Normalised canopy conductance in the ‘Bahianinha’ Navel orchard

plotted against (A) solar radiation (B) water vapour pressure deficit and

(C) air temperature. The forms of the model functions based upon the

optimised parameters are shown as solid lines.


112

B

Vapour pressure deficit (kPa)

0 2 4 6 8

gc/g

c m

ax

0.0

0.2

0.4

0.6

0.8

1.0

1.2

C

Temperature (oC)

0 10 20 30 40

0.0

0.2

0.4

0.6

0.8

1.0

1.2

A

Solar radiation (W m-2)0 200 400 600 800

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Figure 5.10. Normalised canopy conductance in the ‘Rustenburg’ Navel orchard

plotted against (A) solar radiation, (B) water vapour pressure deficit

and (C) air temperature. The forms of the model functions based upon

the optimised parameters are shown as solid lines.


113

Improved correlations were observed between gc predicted by the Jarvis-type model,

using orchard specific parameters (Table 5.2) and measured gc in the ‘Bahianinha’

and ‘Rustenburg’ Navel orchards (Figure 5.11). While there was a good agreement

between predicted and measured transpiration in the ‘Bahianinha’ Navel orchard

using parameters for the Jarvis model specific to this orchard, there were periods of

underestimation of transpiration in the ‘Rustenburg’ Navel orchard during spring of

2010 (August to October) and winter 2011 (April to August) (Figure 5.12).

'Bahianinha' Navel

0 2 4 6 8 10 12 14

0

2

4

6

8

10

12

14

y = 0.8916X

R2 = 0.60

'Rustenburg' Navel

Measured gc (mm s

-1)

0 2 4 6 8 10 12 14 16 18

Pre

dic

ted

gc (

mm

s-1

)

0

2

4

6

8

10

12

14

16

18

y = 0.8797x

R2 = 0.57

1:1 line

1:1 line



in the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards.


114

'Bahianinha' Navel

01

-De

c-0

9

21

-De

c-0

9

10

-Ja

n-1

0

30

-Ja

n-1

0

19-F

eb-1

0

11

-Ma

r-1

0

31

-Ma

r-1

0

20

-Ap

r-1

0

10

-Ma

y-1

0

30

-Ma

y-1

0

19

-Ju

n-1

0

Tra

nsp

iratio

n (

mm

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Predicted

Measured

'Rustenburg' Navel

Date

01

-Aug

-10

31

-Aug

-10

30

-Sep

-10

30

-Oct-

10

29

-Nov-1

0

29

-Dec-1

0

28

-Jan

-11

27

-Feb-1

1

29

-Mar-

11

28

-Apr-

11

28

-May-1

1

27

-Jun

-11

27

-Jul-11

26

-Aug

-11

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Figure 5.12. Time series plot of measured and predicted transpiration in the

‘Bahianinha’ and ‘Rustenburg’ Navel orchards. The gaps in the plotted

data were due to missing hourly weather data caused by power failure

to the weather stations.

Regression analysis revealed reasonable linear relationships between predicted and

measured transpiration in both the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards

(Figure 5.13). The model predicted transpiration reasonably well as almost all the

statistical parameters, except for MAE in the ‘Rustenburg’ Navel orchard, are within

the ranges stipulated by de Jager (1994) for good model performance (Figure 5.13).


115

The MAE, which was greater than 20 % in the ‘Rustenburg’ Navel orchard, was

probably a reflection of the underestimation of transpiration by the model in autumn

and winter (Figure 5.12). The Penman-Monteith equation coupled with Jarvis canopy

conductance model (using orchard specific parameters) underestimated cumulative

transpiration by 13 % in the ‘Delta’ Valencia, 2 % in ‘Bahianinha’ and 18% in the

‘Rustenburg’ Navel orchards over the measurement period (Figure 5.14).

'Bahianinha' Navels

0.0 0.4 0.8 1.2 1.6

Pre

dic

ted tra

nspiration (

mm

)

0.0

0.4

0.8

1.2

1.6

y = 0.99x

R2 = 0.52

MAE = 17.92 %D = 0.88

RMSE = 0.04

Measured transpiration (mm)

0 1 2 3

0

1

2

3

y = 1.092x

R2

= 0.60MAE = 29.73 %

D = 0.81RMSE = 0.24

'Rustenburg' Navels

Figure 5.13. Regression analysis between predicted and measured transpiration in

the ‘Bahianinha’ and ‘Rustenburg’ Navel orchards. Statistical

parameters used include slope of regression equation, coefficient of

determination (R2), mean absolute error (MAE), Willmot coefficient of

agreement (D) and root mean square error (RMSE).


116

'Delta' Valencias

01-Dec 01-Jan 01-Feb 01-Mar 01-Apr 01-May 01-Jun 01-Jul

0

50

100

150

200

250

Measured

Predicted

'Bahianinha' Navels

01-Dec 01-Jan 01-Feb 01-Mar 01-Apr 01-May 01-Jun 01-Jul

Cum

ula

tive tra

nspiration (

mm

)

0

20

40

60

80

100

120

140

160

180

'Rustenburg' Navels

Date

01-Sep 01-Nov 01-Jan 01-Mar 01-May 01-Jul

0

100

200

300

400

500

Figure 5.14. Cumulative measured transpiration and transpiration predicted using a

Jarvis-type model parameterised in the respective orchards for the

measurement periods. The plateau in water use graphs occurring

around April/May in the three graphs is due to periods of missing data.


117

5.4 Discussion

The optimised hourly values of gc max obtained in the three orchards were higher than

the maximum values calculated by inverting the Penman-Monteith equation. The

value of gc max represents the ideal situation at which all functions are equal to one.

In fact the Jarvis model predicts gc max values under conditions of low VPD and high

SR and such conditions do not normally occur in the field (Whitley et al., 2009).

These values were also higher than the 6.98 to 7.96 mm s-1 that was reported by

Oguntunde et al. (2007) in sweet oranges which might mean that this parameter is

not conservative for citrus. However, the gc max obtained for the different orchards by

the optimisation process, followed in this instance, contains artefacts of the gc data

used as well as the parameters of the response functions that were attained.

The parameter kD1 is much lower than the values of 0.116 and -0.229 kPa reported

in poplar trees by Zhang et al. (1997), who used a similar form of the VPD function,

most probably indicating the differences in response of the two species to VPD. The

optimised value for the parameter kT, for optimum temperature, obtained in all three

orchards was slightly lower than 25.5 oC that was established by Oguntunde et al.

(2007). Despite the differences in canopy sizes and different environmental

conditions experienced in the orchards the response functions obtained in three

orchards in this study were very similar.

When the parameters of the Jarvis model were used to predict conductances,

derived from the sap flow data, the model was only able to account for a small

proportion (56 to 60 %) of the variance in gc. The modelling approach first suggested

by Jarvis (1976) has been widely used to predict conductances in fruit trees,

including citrus. The level at which these weather variables were able to explain the

variability in canopy conductance is slightly lower than the 83 % reported by

Oguntunde et al. (2007) in sweet oranges under semi-arid Tropical Monsoon climate,

but higher than 11 % obtained by Cohen and Cohen (1983) after fitting a similar

Jarvis-type model to measured leaf conductance of Shamouti orange trees under

Mediterranean conditions.


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The Penman-Monteith equation coupled with the Jarvis model (with one set of

parameters) was able to predict transpiration successfully in the three orchards over

a relatively long period. This is despite the limitations of Jarvis-type models on days

when the crop canopy is wet, or in cloudy or overcast conditions, that most studies

such as Oguntunde et al. 2007 tend to eliminate from the data set when testing the

approach. A similar modelling approach by Whitely et al. (2009) gave fairly

reasonable results in forest species over a period of 109 days. This modelling

approach may be applicable to semi-arid sub-tropical conditions where wetting of the

canopy by rainfall and occurrence of cloudy/overcast conditions are both infrequent.

The parameters of the Jarvis-type model obtained in the ‘Delta’ Valencia orchard did

not predict transpiration accurately in either the ‘Bahianinha’ or ‘Rustenburg’ Navel

orchards even though they were similar. The multiplicative form of the Jarvis model

means that the differences observed in the parameters are multiplied, hence the

large differences between measured and predicted values when using such an

approach. The fact that transpiration was overestimated in the ‘Bahianinha’ Navel

orchard and underestimated in the ‘Rustenburg’ Navel orchard, although with a

reasonable correlation, might mean that transferring such an approach amongst

orchards is not as straight-forward as proposed previously by Whitehead (1998). For

instance Villalobos et al. (2013) argued that LAI may not be the best parameter to

use when up-scaling transpiration in fruit tree orchards since it is a reflection of the

available, rather than the conducting leaf area. In order for this approach to work a

methodology for determining the leaf area active in transpiration would need to be

formulated.

There are a few possible reasons for the failure of the Jarvis-type parameters

obtained in the ‘Delta’ Valencia to accurately predict transpiration in both the

‘Bahianinha’ and ‘Rustenburg’ Navel orchards. There is evidence that stem hydraulic

conductance varies among rootstock/scion combinations in citrus (Rodríguez-Gamir

et al., 2010), which would have a direct bearing on the variations of canopy

conductance values calculated using the Penman-Monteith equation based on sap

flow measurements. Cultivar effects are probably partly reflected by the fact that

largest difference observed between the kD2 parameters of the VPD response

function was between the ‘Rustenburg’ Navel and ‘Delta’ Valencia trees. The


119

thickness and composition of epicuticular waxes found on citrus that help to

suppress cuticular transpiration vary amongst citrus species, such that the sensitivity

of the cultivars to environmental conditions is also expected to differ (Baker et al.,

1975). Although the findings of Baker et al. (1975) were at species level, the

occurrence of such difference in cultivars and their effect on the regulation of

transpiration (and hence conductance) would be worthy of investigation.

It is also important to note that the response functions of Jarvis-type model depend

upon the physiological condition of the plants, the previous and current season in

which measurements were conducted (Jarvis, 1976). The differences in leaf

resistance brought about by the differences in crop load of these orchards that were

discussed in Chapter 4 would also be expected to manifest at canopy level. The

highest VPD recorded at the Citrusdal site is almost twice that observed at

Groblersdal during the measurement period. Citrus transpiration on which the gc

values were based has been shown to be sensitive to VPD (Oguntunde et al., 2007)

which may mean that the response of the trees under these conditions may have

differed. In addition the maximum solar radiation recorded at the Groblersdal site

was above 1000 W m-2 in both seasons as compared to a maximum of

approximately 800 W m-2 recorded at the Citrusdal site. The ability of citrus trees to

acclimatize to different levels of solar radiation, as reported by Syvertsen (1984),

may also have an effect on the responses of the citrus leaves. Since measurements

of transpiration were conducted for only one season in each orchard, the effects of

conditions in the previous seasons could not be evaluated.

5.5 Conclusion

The use of the Penman-Monteith equation coupled with a Jarvis-type model for

predicting transpiration in citrus orchards was tested. The Jarvis model had response

functions of solar radiation, temperature and vapour pressure deficit. The model was

able to predict long-term variations of citrus transpiration reasonably well only when

parameterized using data from that specific orchard. However, transferability of the

optimised parameters from one orchard to an orchard in a similar or different region

was not possible.


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Chapter 6: General conclusions and recommendations

6.1 Overview of study

Citrus is a one of the most important fruit crops grown across the world, as well as in

South Africa. Production of this evergreen crop in semi-arid countries, which receive

seasonal rainfall, is made possible through irrigation. The advent of micro-irrigation

systems, such as drip, provides an opportunity to match crop water requirements

and irrigation amounts, but needs to be coupled with appropriate water management

techniques (Jones, 2004). Insufficient knowledge of fruit tree water use, under these

relatively new systems, has been identified as a major factor hindering the

application and further development of existing irrigation water management tools in

South Africa (Pavel et al., 2003; Volschenk et al., 2003). This is probably because

measurements of crop water use are time consuming, expensive and require

specialized expertise, which are not always available. The situation is made worse in

orchards, where tree size is variable between different orchards and by the long time

needed to obtain good estimates (Hoffman et al., 1982; Castel et al., 1987). Water

use models have proved very useful in extrapolating measured data and predicting

water use of different crops.

The aims of this study were two-fold: i) to measure long-term transpiration of well

managed micro-irrigated citrus orchards and; ii) to test physically–based models that

can be used to predict transpiration across different citrus growing regions. This

study concentrated on the transpiration component since it forms the larger portion

of orchard water use in micro-irrigated fruit tree orchards (Reinders et al., 2010) and

is directly related to productivity (Villalobos et al., 2013). In order to meet the

objectives, sap flow measurements were performed using the heat ratio method

(HRM) as described by Burgess et al. (2001) in two orchards in South Africa. The

two orchards planted with ‘Delta’ Valencia and ‘Bahianinha’ Navel orange trees were

located in the summer rainfall area. A data set from an orchard planted with

‘Rustenburg’ Navel orange trees that was located in the winter rainfall area was

sourced for model validation. Weather variables, which include solar radiation,

temperature, relative humidity and wind speed, were measured using automatic

weather stations close to the orchards for modelling purposes.


121

6.2 Calibration of the heat ratio method (HRM) sap flow technique for long-term

transpiration measurement in citrus orchards

The HRM was calibrated against eddy covariance measurements in winter (31July to

3 August 2008) and autumn (21 to 25 May 2009) in the ‘Delta’ Valencia orchard,

when soil evaporation was considered negligible (Chapter 2). Calibration was done

by adjusting the wounding width to ensure that average transpiration of sample trees

matched crop evapotranspiration (ETc) measured above the orchard using the eddy

covariance method. The virtual wound widths that matched mean transpiration of

sample trees to ETc for winter and autumn periods were 3.3 and 3.1 mm,

respectively. The similarity of the virtual wound widths obtained during the two

measurement periods (winter and autumn) and the subsequent successful use of an

average value (3.2 mm) suggests that wounding does not increase with time and a

single field calibration of the HRM using eddy covariance measurements is sufficient

for measuring transpiration in citrus orchards. The requirement for a wound width

greater than the observed 2 mm width in citrus was necessitated by the fact that

citrus had non-homogeneous functional wood as determined by the anatomical

assessments. Non-homogeneity of wood means that the ideal heat pulse theory will

not apply to this wood and a correction factor is therefore required. This is in

agreement with previous studies in kiwifruit (Green and Clothier, 1988) and citrus

(Fernández et al., 2006). In addition citrus wood reacted to drilling and heating by

deposition of phenols and gums that caused xylem blockages which extended

beyond what could be seen by the naked eye, as revealed by the anatomical

assessments in this study. Once the calibration of the HRM was performed, the

method was then used to quantify transpiration in the three orchards.

6.3 Measurement of long-term transpiration and transpiration coefficients in

citrus orchards

In order to address the problem of lack of information of water use in citrus orchards,

which was previously highlighted (Pavel et al., 2003; Volschenk et al., 2003), the

HRM was employed to quantify long-term transpiration rates in three citrus orchards

(Chapter 3). Average daily transpiration in the three orchards ranged from 0.77 mm

day-1 to 2.26 mm day-1 depending on canopy size, season and climate (summer

versus winter rainfall areas). Total seasonal transpiration for the two orchards in


122

which measurements covered an entire production season, i.e. ‘Delta’ Valencia and

‘Rustenburg’ Navel orchards were 682 mm and 672 mm, respectively. This study

confirmed the variations of transpiration in citrus orchards as previously reported

(García Petillo and Castel, 2007). Whilst the measurement of transpiration in the

three orchards is not exhaustive of all orchard conditions in South Africa, it does

provide a basis for the understanding of the drivers of transpiration. Sap flow-based

measurements of transpiration obtained in this study presented a valuable data set

for testing models of citrus transpiration that can be used to extrapolate measured

transpiration to other growing regions of the world.

Transpiration coefficients (Kt) determined in the three orchards ranged between 0.28

and 0.71. The Kt values were almost constant throughout the seasons in the summer

rainfall area, and significantly higher in the winter months than in the summer months

in the winter rainfall area. This indicated that transpiration does not increase at the

same rate as reference evapotranspiration (ETo) during the summer months and

confirmed the existence of strong regulation mechanisms within the citrus tree

hydraulic path that was previously reported (van Bavel et al. 1967; Kriedemann and

Barrs 1981; Sinclair and Allen 1982). It is also indicative of fact that citrus trees are

only able to supply a certain maximum amount of water to the canopy at high ETo (≥

5 mm day-1), even when soil water is not limiting, as suggested by Sinclair and Allen

(1982).

Differences in measured Kt values between the orchards in Groblersdal, despite

similar ETo in both years, suggests an effect of canopy size on transpiration. On the

other hand differences in the trends of Kt values between the two orchards located in

Groblersdal and the one in Citrusdal in winter could be linked to differences in VPD.

Vapour pressure deficit was reported as the dominant regulator of transpiration of

citrus by Kriedemann and Barrs (1981) and Oguntunde et al. (2007) when soil water

is not limiting. The clear differences between Kt values in the three orchards and

those published in literature (including the FAO56) indicate that the Kt values are

orchard specific. This result confirmed the variation of Kt values of citrus orchards

reported previously (Rana et al. 2005; Villalobos et al., 2009; Marin and Angelocci,

2011; Villalobos et al., 2013). Crop coefficients determined in one orchard can

therefore not be directly applied or transferred to different growing regions of the


123

world. This emphasizes the need to develop an easy method for estimating site-

specific crop coefficients, in order to improve water management in citrus orchards.

6.4 Estimation of transpiration coefficients from plant height and canopy cover

The significance of the role of the resistance to water transport within the citrus tree

transpiration stream was highlighted during the development Kt values based on

crop height and canopy cover following the method suggested by Allen and Pereira

(2009) (Chapter 4). Good agreements between measured and estimated Kt values

were only obtained after back-calculating leaf resistance (rl) using measured

transpiration values, as recommended by Allen and Pereira (2009). This study

established that the leaf resistance of citrus may be higher than what was suggested

by Allen and Pereira (2009) for a generic citrus orchard. The rl values of ranging from

419 to 2 694 s m−1 obtained through this procedure were comparable to those

ranging from 200 to 8 280 s m−1 reported in literature (Cohen and Cohen 1983;

Dzikiti et al. 2007; Pérez-Pérez et al., 2008). It was also established that contrary to

the constant rl value (420 s m-1) suggested by Allen and Pereira (2009), leaf

resistance increased for all orchards during the summer period. Allen and Pereira

(2009) recommended that improvements in estimating the rl term are needed to

improve the accuracy of the methodology. In that regard a relationship between

mean monthly rl and ETo in the ‘Rustenburg’ Navel orchard provided a means of

estimating mean leaf resistance, which estimated Kt values with a reasonable degree

of accuracy in the three orchards. However, this relationship only provided good

seasonal estimates of transpiration, which means that it can only be useful for

irrigation planning. A more mechanistic model capable of capturing the dynamics of

the canopy conductance in citrus varieties is required to predict transpiration of citrus

trees on day-to-day basis for purposes such as irrigation scheduling.

6.5 Predicting transpiration of citrus orchards using the Penman-Monteith

equation coupled with a Jarvis-type canopy conductance model

The use of a more mechanistic approach that incorporates a dynamic canopy

conductance term was also tested (Chapter 5). This was in the form of the Penman-

Monteith equation, coupled with the estimation of canopy conductance using a

Jarvis-type model, as proposed by Oguntunde et al. (2007). It was demonstrated that


124

once optimised a single set of response functions for canopy conductance, obtained

in each orchard, can be used to predict transpiration accurately in the respective

orchard for periods over six months. This approach may be applicable to sub-tropical

conditions where wetting of the canopy by rainfall and occurrence of cloudy/overcast

conditions are both infrequent. This result is similar to what was established by

Whitely et al. (2009) who also reported that this approach could be applied in a forest

species for a fairly long time. The ability of a single set of response functions to

predict transpiration when the Jarvis-type model was parameterized using data in the

respective orchards does put hope in the method as a way of mechanistically

predicting citrus transpiration. It was also shown that the parameters of the Jarvis

model obtained in an orchard in the summer rainfall are not suitable for predicting

conductance (and hence transpiration) in the same or different region. This was

attributed to the fact that the parameters obtained in one orchard contain artifacts of

the measured data that may not exist in the other orchards. The factors that could

potentially influence these parameters and hinder the transferability of the Jarvis-

type model, which could not be ascertained in this study, include differences in

varieties, climatic conditions and crop load. This approach will only be applicable if

parameterized with measured data.

6.6 Recommendations for future research

Knowledge of water use of citrus orchards is crucial for irrigation planning and

management. In this study transpiration of three citrus orchards was measured, and;

the data was used to test some of the models that can be used to estimate water use

in these orchards. Nevertheless, questions related to water use of citrus orchards

still remain unanswered. Measurements of transpiration in three orchards presented

in this study are not exhaustive on how much water use is used by citrus under all

environmental conditions and management strategies in South Africa. Measurement

of transpiration should be conducted in different growing regions under the different

strategies to consolidate the base information of citrus orchard transpiration attained

in this study. Such monitoring experiments should aim to address water use of the

trees in relation to factors possibly impacting transpiration e.g. canopy size,

rootstock/scion combinations and crop load. Citrus water use measurements should

be conducted simultaneously with environmental monitoring to allow for further


125

improvement of the modelling approaches that were evaluated in this study. There is

room for improvement in the estimation of the rl term so as to use the method

predicting transpiration on daily time scale. The approach for transferring the Jarvis-

type model amongst orchards needs further research. A starting point would be to

determine a maximum canopy conductance value of citrus that is independent of the

measured transpiration data for parameterization of such a model. Information on

water use of specific rootstock/scion combinations obtained for long periods covering

consecutive seasons can also be used to answer question pertaining to the

transferability of Jarvis-type canopy conductance model amongst different varieties

that arose in this study. The exploration of other modelling approaches such as a

combination of a crop coefficient and a maximum transpiration rate as envisaged by

Sinclair and Allen (1982) should be considered as well. Using such a model, it will be

important to be able to determine what the maximum transpiration rate would be for

a certain sized canopy, which may be addressed by way of extensive measurements

mentioned above.


126

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